Written by Chris Jackson, Ed.D. Algebra I EOC 10-Day REVIEW Written by Chris Jackson, Ed.D. www.hedgehoglearning.com © Hedgehog Learning

Algebra I EOC Review All clipart and images used in this review are either created by Hedgehog Learning, found in public domain, or used with permission from iStockphoto, iClipart, Microsoft, or www.123rf.com © Hedgehog Learning

Algebra I EOC Review DAY 1 Functional Relationships READINESS STANDARD – TEKS A.1D and A.1E READINESS STANDARDS A.1D – represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities A.1E – interpret and make decisions, predictions, and critical judgments from functional relationships © Hedgehog Learning

Relationships On the Algebra I EOC, you will see relationships in the form of: Tables Graphs Inequalities Mapping Models Equations Verbal Descriptions Diagrams © Hedgehog Learning

Representing Relationships Imagine the following scenario and apply several representations to it: Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. © Hedgehog Learning

Representing Relationships Imagine the following scenario and apply several representations to it: Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. WRITE AN EQUATION TO REPRESENT THIS RELATIONSHIP. x = number of weeks y = total number of cards © Hedgehog Learning

Representing Relationships Imagine the following scenario and apply several representations to it: Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. Is this what you wrote? y = 25x + 350 © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. EQUATION y = 25x + 350 Total number of baseball cards in his collection. © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. EQUATION y = 25x + 350 Total number of baseball cards in his collection. Number of weeks he adds to his collection. © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. EQUATION y = 25x + 350 Number of cards he adds to his collection each week Total number of baseball cards in his collection. Number of weeks he adds to his collection. © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. EQUATION y = 25x + 350 Number of cards he adds to his collection each week Number of cards his dad gave him to start his collection Total number of baseball cards in his collection. Number of weeks he adds to his collection. © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. TABLE y = 25x + 350 x Number of Weeks y Total Number of Cards Now create a data table for the total number of cards his has collected for every week. © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. TABLE y = 25x + 350 x Number of Weeks y Total Number of Cards 1 375 © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. TABLE y = 25x + 350 x Number of Weeks y Total Number of Cards 350 1 375 2 400 3 425 5 475 10 600 20 850 © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. GRAPH y = 25x + 350 x y 1 375 2 400 3 425 5 475 10 600 20 850 Now create a graph to represent the data in the equation and table. © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. GRAPH y = 25x + 350 x y 1 375 2 400 3 425 5 475 10 600 20 850 © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. MAPPING y = 25x + 350 Now create a mapping model of the relationship. x y © Hedgehog Learning

Representing Relationships Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. MAPPING y = 25x + 350 Now create a mapping model of the relationship. x y 1 2 3 4 350 375 400 425 450 © Hedgehog Learning

Representing Relationships Five ways to represent this relationship: Verbal, Equation, Table, Mapping, and Graph. Steven wants to start collecting baseball cards. His dad bought him his first set which includes 350 cards. Every week, he takes a portion of his allowance and buys 25 more cards to add to his collection. y = 25x + 350 © Hedgehog Learning

Algebra I EOC Review DAY 2 Properties and Attributes of Functions READINESS STANDARD – TEKS A.2B READINESS STANDARD 2.B identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete © Hedgehog Learning

Domain and Range Domain All possible x-values for a function Range All possible y-values for a function DOMAIN x values RANGE y values © Hedgehog Learning

Domain and Range Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? © Hedgehog Learning

Domain and Range First, let’s set up a function for her earnings. Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? Domain All possible x-values for a function Range All possible y-values for a function First, let’s set up a function for her earnings. We will need to know: Her earnings per hour ($15) The number of hours she can tutor (x) © Hedgehog Learning

Domain and Range f(x) = 15x Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? Domain All possible x-values for a function Range All possible y-values for a function f(x) = 15x What are all the possible values for x? (This is the domain.) © Hedgehog Learning

Domain and Range f(x) = 15x Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? Domain All possible x-values for a function Range All possible y-values for a function f(x) = 15x What are all the possible values for x? (This is the domain.) She can tutor 2 hours per day for 5 days during the week, so the maximum number of hours she can tutor is 10 hours. © Hedgehog Learning

Domain and Range f(x) = 15x 0 ≤ x ≤ 10 Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? Domain All possible x-values for a function Range All possible y-values for a function f(x) = 15x Therefore, the DOMAIN is: 0 ≤ x ≤ 10 © Hedgehog Learning

Domain and Range f(x) = 15x 15(0) ≤ f(x) ≤ 15(10) Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? Domain All possible x-values for a function Range All possible y-values for a function f(x) = 15x If the DOMAIN is 0 ≤ x ≤ 10, then what is the RANGE? 15(0) ≤ f(x) ≤ 15(10) © Hedgehog Learning

Domain and Range f(x) = 15x 0 ≤ f(x) ≤ 150 Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? Domain All possible x-values for a function Range All possible y-values for a function f(x) = 15x If the DOMAIN is 0 ≤ x ≤ 10, then what is the RANGE? 0 ≤ f(x) ≤ 150 © Hedgehog Learning

Domain and Range Domain 0 ≤ x ≤ 10 Range 0 ≤ f(x) ≤ 150 f(x) = 15x Maria tutors Algebra after school for $15 per hour. Her tutoring hours are from 4:00 – 6:00 PM, Monday – Friday. What are the domain and range values for a function representing her potential earnings this week? f(x) = 15x Domain All possible x-values for a function 0 ≤ x ≤ 10 Range All possible y-values for a function 0 ≤ f(x) ≤ 150 © Hedgehog Learning

Domain and Range What is the domain and range of the graph below? © Hedgehog Learning

Domain and Range What is the domain and range of the graph below? -7 ≤ x ≤ 6 DOMAIN © Hedgehog Learning

Domain and Range What is the domain and range of the graph below? -7 ≤ x ≤ 6 RANGE 2 ≤ y ≤ 7 RANGE © Hedgehog Learning

Domain and Range What is the domain and range shown below? x y -4 3 5 8 -2 1 9 © Hedgehog Learning

Domain and Range What is the domain and range shown below? x y -4 3 5 8 -2 1 9 DOMAIN values RANGE values © Hedgehog Learning

Domain and Range What is the domain and range shown below? x y DOMAIN {-4, 0, 3, 5, 8} RANGE {-2, 1, 9} -4 3 5 8 -2 1 9 DOMAIN values RANGE values © Hedgehog Learning

Algebra I EOC Review DAY 3 Properties and Attributes of Functions READINESS STANDARD – TEKS A.2D READINESS STANDARD 2.D collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations © Hedgehog Learning

Scatterplots SCATTERPLOTS are data points plotted on a graph. Usually these data points represent real data collected through an investigation or experiment. Mathematicians will identify if the scatterplot demonstrates a type of relationship. The graph is real data representing the age of married couples. Is there a relationship? (No pun intended!) © Hedgehog Learning

Scatterplots Let’s look at real-life scatterplots and determine if the relationship is: No relationship Positive correlation Negative correlation © Hedgehog Learning

Scatterplots Source: Boston Globe No relationship, positive correlation, or negative correlation? © Hedgehog Learning

Scatterplots POSITIVE CORRELATION Source: Boston Globe © Hedgehog Learning

Scatterplots Source: Texas Hurricane No relationship, positive correlation, or negative correlation? © Hedgehog Learning

Scatterplots NO RELATIONSHIP Source: Texas Hurricane © Hedgehog Learning

Scatterplots Source: Math Captian No relationship, positive correlation, or negative correlation? © Hedgehog Learning

Scatterplots NEGATIVE CORRELATION Source: Math Captain © Hedgehog Learning

Algebra I EOC Review DAY 4 Properties and Attributes of Functions READINESS STANDARD – TEKS A.4A READINESS STANDARD 4.A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations © Hedgehog Learning

Finding a Function Value On the Algebra I EOC, you will likely be given a scenario where you must find the function to solve problem. A classic example of this is finding the side of a rectangle, x, given the perimeter. 3x What is the value of x? x Perimeter = 32 inches © Hedgehog Learning

Finding a Function Value 3x What is the value of x? x Perimeter = 32 inches Setup the function: 2(width) + 2(length) = Perimeter 2(x) + 2(3x) = 32 © Hedgehog Learning

Finding a Function Value 3x What is the value of x? x Perimeter = 32 inches Setup the function: 2(x) + 2(3x) = 32 2x + 6x = 32 8x = 32 x = 4 © Hedgehog Learning

Finding a Function Value 3x x 4 inches Perimeter = 32 inches 12 inches © Hedgehog Learning

Simplifying Polynomials Simply the following polynomial: 4x2 + 3(x – 2) – 2x(x + 1) © Hedgehog Learning

Simplifying Polynomials Simply the following polynomial: 4x2 + 3(x – 2) – 2x(x + 1) Step 1: Multiply the coefficients on the parenthesis. © Hedgehog Learning

Simplifying Polynomials Simply the following polynomial: 4x2 + 3(x – 2) – 2x(x + 1) 4x2 + 3x – 6 – 2x2 – 2x Step 2: Group like terms and combine. © Hedgehog Learning

Simplifying Polynomials Simply the following polynomial: 4x2 + 3(x – 2) – 2x(x + 1) 4x2 + 3x – 6 – 2x2 – 2x 2x2 + x – 6 © Hedgehog Learning

Algebra I EOC Review DAY 5 Linear Functions READINESS STANDARD – TEKS A.5C READINESS STANDARD 5.C use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. Write a linear function to calculate the total profit from the cookie sale. © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. Let’s make: x = the number of cookies, and f(x) = the total profit. © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. We know f(x) (profit) is going to be a function of x (cookies sold) There will be $2 donation no matter how many cookies purchased. Every cookie will be $1.50, or 1.50x. The profit will be 75% of the total sales, or 0.75. © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. Let’s write the function: f(x) = 0.75 ( 2.00 + 1.50x ) © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. Let’s write the function: f(x) = 0.75 ( 2.00 + 1.50x ) 75% of Sales $2 Donation $1.50 per cookie (x) © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. Now, create a table representing profit as a function of the number of cookies sold in quantities of 10, 80, and 200 Profit f(x) Cookies Sold (x) 10 80 200 © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. f(x) = 0.75 ( 2.00 + 1.50x ) Profit f(x) Cookies Sold (x) $12.75 10 $91.50 80 $226.50 200 © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. Complete a graph representing this linear relationship. © Hedgehog Learning

Making Connections with Linear Functions Consider this situation: Eric is selling cookies for a bake sale for his youth group. There is a $2 donation for every purchase, and the price of each cookie is $1.50. After expenses, Eric’s youth group makes 75% profit of the total sales. Complete a graph representing this linear relationship. © Hedgehog Learning

Algebra I EOC Review DAY 6 Linear Functions READINESS STANDARD – TEKS A.6B READINESS STANDARD 6.B interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs © Hedgehog Learning

Slope and Intercepts y2 – y1 x2 – x1 Slope (m) = SLOPE - number that describes both the direction and the steepness of the line y2 – y1 x2 – x1 Slope (m) = INTERCEPT – point at which a line crosses the x-axis or y-axis y-intercept x-intercept © Hedgehog Learning

Slope and Intercepts y = mx +b Any line can be identified by the slope of the line (m) and the point at which it intersects the y-axis (b). In terms of x and y, the equation for a line is: y = mx +b © Hedgehog Learning

Slope and Intercepts Write the equation for the line shown in the graph in y = mx + b format. © Hedgehog Learning

Slope and Intercepts Write the equation for the line shown in the graph in y = mx + b format. slope = 1 y-Intercept = 5 y = x + 5 © Hedgehog Learning

Slope and Intercepts What would be the graph of the following? y = -2x – 2 © Hedgehog Learning

Slope and Intercepts What would be the graph of the following? y = -2x – 2 © Hedgehog Learning

Slope and Intercepts Identify the slope and y-intercept of the graph. © Hedgehog Learning

Slope and Intercepts y-intercept = - 1 y = − 𝟏 𝟐 x – 1 Identify the slope and y-intercept of the graph. Slope = − 𝟏 𝟐 y-intercept = - 1 y = − 𝟏 𝟐 x – 1 © Hedgehog Learning

Slope and Intercepts x y Identify the slope and y-intercept of the data table? x y 5 2 6 4 7 9 © Hedgehog Learning

Slope and Intercepts x y Identify the slope and y-intercept of the data table? 𝒎= 𝒚𝟐 −𝒚𝟏 𝒙𝟐 −𝒙𝟏 𝒎= 𝟖 −𝟓 𝟔 −𝟎 𝒎= 𝟑 𝟔 or 𝒎= 𝟏 𝟐 x y 5 2 6 4 7 8 y-intercept = 5 𝒚= 𝟏 𝟐 𝒙+𝟓 © Hedgehog Learning

Algebra I EOC Review DAY 7 Linear Functions READINESS STANDARD – TEKS A.6C and A.6F READINESS STANDARDS 6.C investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b 6.F interpret and predict the effects of changing slope and y‐intercept in applied situations © Hedgehog Learning

Changing Slope y = mx + b y = x In the linear equation m is the slope. Let’s change m on the graph with the equation y = x. y = x © Hedgehog Learning

Changing Slope y = 𝟏 𝟑 x y = 𝟏 𝟐 x y = x y = 2x y = 3x © Hedgehog Learning

Changing Slope y = 𝟏 𝟑 x y = 𝟏 𝟐 x y = x y = 2x y = 3x © Hedgehog Learning

Changing Slope y = 𝟏 𝟑 x y = 𝟏 𝟐 x y = x y = 2x y = 3x © Hedgehog Learning

Changing Slope y = 𝟏 𝟑 x y = 𝟏 𝟐 x y = x y = 2x y = 3x © Hedgehog Learning

Changing y-Intercept y = mx + b y = 𝟏 𝟐 x In the linear equation b is the y-intercept. Let’s investigate a change in b on the graph. y = 𝟏 𝟐 x © Hedgehog Learning

Changing y-Intercept y = 𝟏 𝟐 x y = 𝟏 𝟐 x + 4 © Hedgehog Learning

Changing y-Intercept y = 𝟏 𝟐 x y = 𝟏 𝟐 x + 4 y = 𝟏 𝟐 x – 4 © Hedgehog Learning

Changing Slope and y-Intercept In the linear equation y = -2x +1, the slope multiplied by - 1 2 and the y-intercept is tripled. What is the resulting new linear equation? © Hedgehog Learning

Changing Slope and y-Intercept Original Line: y = -2x + 1 New m = -2 ( - 1 2 ) m = 1 New b = 1 (3) b = 3 © Hedgehog Learning

Changing Slope and y-Intercept Original Line: y = -2x + 1 New m = -2 ( - 1 2 ) m = 1 New b = 1 (3) b = 3 New Line: y = x + 3 © Hedgehog Learning

Algebra I EOC Review DAY 8 Linear Equations and Inequalities READINESS STANDARD – TEKS A.7B READINESS STANDARD 7.B investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities © Hedgehog Learning

Solving Equations and Inequalities The total charge to Mr. Smith from Lawn Works for mowing is $57. Lawn Works charges $25 setup fee plus $8 per hour per person. Two crew members mowed Mr. Smith’s lawn that day. How many hours did it take it take them? © Hedgehog Learning

Solving Equations and Inequalities The total charge to Mr. Smith from Lawn Works for mowing is $57. Lawn Works charges $25 setup fee plus $8 per hour per person. Two crew members mowed Mr. Smith’s lawn that day. How many hours did it take it take them? Step 1: Identify the Variables. y = Total Charge x = Number of Hours m = Number of Mowers © Hedgehog Learning

Solving Equations and Inequalities The total charge to Mr. Smith from Lawn Works for mowing is $57. Lawn Works charges $25 setup fee plus $8 per hour per person. Two crew members mowed Mr. Smith’s lawn that day. How many hours did it take it take them? Step 2: Setup the equation. y = 25 + 8mx 57 = 25 + 8(2)(x) © Hedgehog Learning

Solving Equations and Inequalities The total charge to Mr. Smith from Lawn Works for mowing is $57. Lawn Works charges $25 setup fee plus $8 per hour per person. Two crew members mowed Mr. Smith’s lawn that day. How many hours did it take it take them? Step 3: Solve the equation. 57 = 25 + 8(2)(x) 57 = 25 + 16x x = 2 hours © Hedgehog Learning

Solving Equations and Inequalities Is the point (3, 2) a possible solution for the following inequality? y > 4 – 2x © Hedgehog Learning

Solving Equations and Inequalities Is the point (3, 2) a possible solution for the following inequality? y > 4 – 2x Step 1: Draw the graph. y= -2x + 4 © Hedgehog Learning

Solving Equations and Inequalities Is the point (3, 2) a possible solution for the following inequality? y > 4 – 2x Step 2: Identify the solution area for the inequality. y > -2x + 4 y > -2x + 4 © Hedgehog Learning

Solving Equations and Inequalities Is the point (3, 2) a possible solution for the following inequality? y > 4 – 2x Step 3: Find the point (3, 2). y > -2x + 4 (3, 2) © Hedgehog Learning

Solving Equations and Inequalities Is the point (3, 2) a possible solution for the following inequality? y > 4 – 2x Step 3: Find the point (3, 2). Yes – (3, 2) is a solution to y > -2x + 4 (3, 2) © Hedgehog Learning

Algebra I EOC Review DAY 9 Linear Equations and Inequalities READINESS STANDARD – TEKS A.8B READINESS STANDARD 8.B solve systems of linear equations using concrete models, graphs, tables, and algebraic methods © Hedgehog Learning

System of Equations Consider these two equations: y1 = x1 + 2 Is there any value for y and x that would solve both equations? © Hedgehog Learning

System of Equations PARALLEL LINES = NO SOLUTION No (x, y) solution to both equations. Key Point: If two equations have the SAME SLOPE, there will be no solution to the system of equations. PARALLEL LINES = NO SOLUTION © Hedgehog Learning

System of Equations PARALLEL LINES = NO SOLUTION No (x, y) solution to both equations. Key Point: If two equations have the SAME SLOPE, there will be no solution to the system of equations. PARALLEL LINES = NO SOLUTION © Hedgehog Learning

System of Equations Consider these two equations: y1 = -2x1 + 2 Is there any value for y and x that would solve both equations? © Hedgehog Learning

System of Equations Yes – The solution set is the point at which the two lines intersect. POINT OF SOLUTION © Hedgehog Learning

System of Equations What is the solution to the following equations? 2y = x + 1 y + 7 = 2x © Hedgehog Learning

System of Equations What is the solution to the following equations? 2y = x + 1 y + 7 = 2x Step 1: Solve for x in the first equation. x = 2y – 1 © Hedgehog Learning

System of Equations What is the solution to the following equations? 2y = x + 1 y + 7 = 2x Step 2: Substitute for x in the second equation. x = 2y – 1 y + 7 = 2 x © Hedgehog Learning

System of Equations What is the solution to the following equations? 2y = x + 1 y + 7 = 2x Step 3: Solve for y. y + 7 = 2(2y – 1) y + 7 = 4y – 2 9 = 3y y = 3 © Hedgehog Learning

System of Equations What is the solution to the following equations? 2y = x + 1 y + 7 = 2x Step 4: Insert the value for y in the first equation and solve for x. 2(3) = x + 1 6 = x + 1 x = 5 © Hedgehog Learning

Algebra I EOC Review DAY 10 Quadratics and Other Nonlinear Functions READINESS STANDARD – TEKS A.9D and A.10A READINESS STANDARDS 9.D analyze graphs of quadratic functions and draw conclusions   10.A solve quadratic equations using concrete models, tables, graphs, and algebraic methods © Hedgehog Learning

Quadratic Equations Quadratic relationships occur when the x-value is squared. Example y = x2 © Hedgehog Learning

Quadratic Equations Quadratic relationships occur when the x-value is squared. Example y = x2 Example y = -x2 © Hedgehog Learning

Quadratic Equations Parts of a Quadratic Graph: Vertex – highest or lowest point of a quadratic graph. Axis of Symmetry y-intercepts x-intercepts (roots) Axis of Symmetry) X-Intercepts (Roots) Y-Intercept Vertex © Hedgehog Learning

Quadratic Equations To find the vertex of a quadratic equation, use the following equation: y = ax2 + bx + c Vertex x-value = −𝑏 2𝑎 © Hedgehog Learning

Solving Quadratic Equations Find the solutions to the following equation: x2 – 36 = 0 © Hedgehog Learning

Solving Quadratic Equations Find the solutions to the following equation: x2 – 36 = 0 x = {-6, 6} (-6)2 – 36 = 0 and (6)2 – 36 = 0 © Hedgehog Learning

Written by Chris Jackson, Ed.D. Algebra I EOC 10-Day Review Best wishes on your Algebra I EOC! You will do great! Written by Chris Jackson, Ed.D. www.hedgehoglearning.com © Hedgehog Learning