ALGEBRA 2 10/23/14 REVIEW FOR TEST 2 (NON-CALCULATOR SECTION) What you’ll learn and why… I can learn how to solve the problems in the Practice Test so.

Slides:



Advertisements
Similar presentations
ON TARGET 4NW OBJECTIVES. ON TARGET Which equation is true for ALL values? This is a calculator problem. One at a time, key each equation into the Y=
Advertisements

LIAL HORNSBY SCHNEIDER
Quadratic Functions.
If the leading coefficient of a quadratic equation is positive, then the graph opens upward. axis of symmetry f(x) = ax2 + bx + c Positive #
§ 8.3 Quadratic Functions and Their Graphs.
§ 8.3 Quadratic Functions and Their Graphs. Graphing Quadratic Functions Blitzer, Intermediate Algebra, 5e – Slide #2 Section 8.3 The graph of any quadratic.
Algebra 2 Chapter 5 Notes Quadratic Functions.
1.5 Transformations of Some Basic Curves 1 In previous sections, we have graphed equations such as f(x)=x 2 +3 by either translating the basic function.
Quadratic Functions, Quadratic Expressions, Quadratic Equations
Quadratic Functions and their graphs Lesson 1.7
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 3 Polynomial and Rational Functions Copyright © 2013, 2009, 2005 Pearson Education, Inc.
Solving Quadratic Equations by Graphing
Algebra 2 10/23/14 Review for Test 2 (non-calculator section)
Simplify each expression.
Graphing Quadratic Functions
Mathematics Quadratic Formula Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement Fund Department.
6.1 Solving Quadratic Equations by Graphing Need Graph Paper!!!
Using the Quadratic Formula to Solve a Quadratic Equation
Unit 5 Quadratics. Quadratic Functions Any function that can be written in the form.
Copyright © Cengage Learning. All rights reserved. Quadratic Equations, Quadratic Functions, and Complex Numbers 9.
Quadratics       Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle.
Chapter 10 Quadratic Equations and Functions
Review for EOC Algebra. 1) In the quadratic equation x² – x + c = 0, c represents an unknown constant. If x = -4 is one of the solutions to this equation,
Graph quadratic equations. Complete the square to graph quadratic equations. Use the Vertex Formula to graph quadratic equations. Solve a Quadratic Equation.
QUADRATIC FUNCTIONS AND INEQUALITIES
1Higher Maths Quadratic Functions. Any function containing an term is called a Quadratic Function. The Graph of a Quadratic Function 2Higher Maths.
Solving Quadratic Equations by the Quadratic Formula
Algebra 2 Chapter 5 Notes Quadratic Functions.
1. Determine if f(x) has a minimum or maximum 2. Find the y-intercept of f(x) 3. Find the equation of the axis of symmetry of f(x) 4. Find the vertex of.
Quadratic Functions. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups, as shown in the graph below. If the coefficient.
§ 8.3 Quadratic Functions and Their Graphs. Blitzer, Intermediate Algebra, 4e – Slide #48 Graphing Quadratic Functions Graphs of Quadratic Functions The.
Copyright © 2011 Pearson Education, Inc. Quadratic Functions and Inequalities Section 3.1 Polynomial and Rational Functions.
Sketching quadratic functions To sketch a quadratic function we need to identify where possible: The y intercept (0, c) The roots by solving ax 2 + bx.
CHAPTER 5 EXPRESSIONS AND FUNCTIONS GRAPHING FACTORING SOLVING BY: –GRAPHING –FACTORING –SQUARE ROOTS –COMPLETING THE SQUARE –QUADRATIC FORMULA.
1. Write 15x2 + 6x = 14x2 – 12 in standard form.
Lesson 7.5.  We have studied several ways to solve quadratic equations. ◦ We can find the x-intercepts on a graph, ◦ We can solve by completing the square,
Quadratic Formula Sam Scholten. Graphing Standard Form Graphing Standard form: Standard form in Quadratic functions is written as: Y = ax 2 +bx+c. The.
Today in Pre-Calculus Go over homework Notes: –Quadratic Functions Homework.
Polynomial Functions Quadratic Functions and Models.
Lesson 10-1 Graphing Quadratic Functions. Objectives Graph quadratic functions Find the equation of the axis of symmetry and the coordinates of the vertex.
Algebra 2: Unit 5 Continued
Solving Quadratic Equations by Graphing 4 Lesson 10.2.
SWBAT…analyze the characteristics of the graphs of quadratic functions Wed, 2/15 Agenda 1. WU (10 min) 2. Characteristics of quadratic equations (35 min)
Algebra 2 Notes (9-4) Graphs of Quadratic Functions.
Lesson 5 Contents Example 1Two Rational Roots Example 2One Rational Root Example 3Irrational Roots Example 4Complex Roots Example 5Describe Roots.
Graphs of Quadratics Let’s start by graphing the parent quadratic function y = x 2.
Lesson 1 Contents Example 1Graph a Quadratic Function Example 2Axis of Symmetry, y-Intercept, and Vertex Example 3Maximum or Minimum Value Example 4Find.
Copyright © Cengage Learning. All rights reserved. 4 Quadratic Functions.
CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.
Do Now: Solve the equation in the complex number system.
Quadratic Functions A quadratic function is described by an equation of the following form: ax² + bx + c, where a ≠ 0 The graphs of quadratic functions.
CHAPTER 5 EXPRESSIONS AND FUNCTIONS GRAPHING FACTORING SOLVING BY: –GRAPHING –FACTORING –SQUARE ROOTS –COMPLETING THE SQUARE –QUADRATIC FORMULA.
Section 3.1 Day 2 – Quadratic Functions After this section you should be able to: Graph a quadratic function with and without a calculator. Find the coordinates.
Imaginary Numbers Review Imaginary Numbers Quadratic Forms Converting Standard Form.
Algebra-2 Section 6-6 Solve Radical Functions. Quiz Are the following functions inverses of each other ? (hint: you must use a composition.
Unit 10 – Quadratic Functions Topic: Characteristics of Quadratic Functions.
Quadratic Functions Sections Quadratic Functions: 8.1 A quadratic function is a function that can be written in standard form: y = ax 2 + bx.
Graphing Parabolas and Completing the Square. Warm-Up Solve each quadratic below (Hint: When you take the square-root you will get 2 answers; one positive.
Chapter 9 Quadratic Equations And Functions By Chris Posey and Chris Bell.
Quadratic Functions PreCalculus 3-3. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups, as shown in the graph below.
Factor each polynomial.
Graphing Quadratic Functions Solving by: Factoring
Splash Screen.
Solve a quadratic equation
Quadratic and Other Nonlinear Inequalities
Y Label each of the components of the parabola A: ________________ B: ________________ C: ________________ C B B 1 2.
SECTION 9-3 : SOLVING QUADRATIC EQUATIONS
Section 9.2 Solving Inequalities with Squares
Day 146 – Solve
Presentation transcript:

ALGEBRA 2 10/23/14 REVIEW FOR TEST 2 (NON-CALCULATOR SECTION) What you’ll learn and why… I can learn how to solve the problems in the Practice Test so I can ace Test 2 on Monday. HW : Know the formulas and methods needed to solve each problem in the Practice Test. Warm-up: 1.Silently recite the Quadratic Formula 5x. 2.Silently recite the formula to find the x- coordinate of the vertex of a quadratic equation in standard form 5x.

The product of complex conjugates is always a real number. From this information, choices C and D should be eliminated. The answer is B 20. Your Turn: Answer Practice Test #1.

Notes: To subtract a complex number, add its opposite. Answer: C Your Turn: Answer Practice Test #2

3. Find the domain and range of each function. A D: R: B D: R: C D: R: D D: R: All real numbers Notes: The domain of a function is the set of all possible x values. The range of a function is the set of all possible y values.

3. To find the y-coordinate of the vertex, substitute the value of x into the original function. The statement which is not true is D. The vertex is at (1, 4) Your Turn: Answer Practice Test #4.

A.-7 B.-11 C. 7 D. 11 Alternative Method: You could use completing the square to convert from standard form to vertex form. Your Turn: Answer Practice Test #5

Subtract 3 from each side Divide each side by 16. Note: Eliminate answers that are not in simplest form. Choices A and B are eliminated because they have a radical in the denominator. The choices left are C and D. C has nonreal solutions while D has real solutions. Simplify.

The answer is C. Your Turn: Answer Practice Test #7.

Subtract 81 from each side. The answer is B. Your Turn: Answer Practice Test #8.

Which function has a greater negative x-intercept? A.Function A B.Function B C.The x-intercepts are equal. Solution: You need to find the negative x-intercepts of both function and then compare to find the greater number. The negative x-intercept of Function B is -1. Use factoring to find the x-intercepts of Function A. (Other methods may be used.) Look for factors of c whose sum is b. Use 5 and -1 Set each factor equal to 0. Solve for x. Your Turn: Answer Practice Test #9.

Steps: Divide each side by the GCF, 5. Subtract 12 from each side. Look for factors of -12 whose sum is 1. Use 4 and -3. Set each factor equal to 0. Solve for x. The answer is C. Your Turn: Answer Practice Test #10. Alternative Method: Work Backwards Substitute the answer choices into the given equation. See which solutions satisfy the given equation.

11. Which of the following functions has its vertex below the x-axis? Solution: To determine which vertex is below the x-axis, graph the vertex of each function. The answer is D. Is there a pattern? What pattern do you see? Given the vertex (h, k), when k < 0, then the vertex is below the x-axis. Your Turn: Answer Practice Test #11. Vertex of A: (0, 0) Vertex of B: (-4, 3) Vertex of C: (0, 2) Vertex of D: (1, -2)

12. What is the equation of the parabola shown? Notes: 1. The parabola opens up, therefore a > 0. Eliminate Choices A and B. 2. USE NICE POINTS! The point (1, 4) is on the parabola. Check by substituting x = 1 and y = 4 into the remaining equations C and D. The answer is D. Your Turn: Answer Practice Test #12.

STEPS 1. Write the original inequality. 2. Set one side of the inequality to 0. (Add 3x and 6 to each side.) 3. Combine like terms. 4. Change the inequality sign to equal sign. 5. Solve the quadratic equation to find the zeros or x-intercepts. 6. Mark the x-intercepts on a numberline. The numberline is now divided into three intervals: A, B, and C. Sketch the parabola. 7. Determine in which interval/s the solutions lie. Write the solution set using the correct inequality symbols. 8. Check by using test values. A B C

14. Which of the following quadratic equations has no real roots? Write in standard form

A.(1, 3); maximum B.(1, 3); minimum C.(3, 1); maximum D.(3, 1); minimum Notes: Since a > 0, the parabola opens up and it has a minimum value. Eliminate Choices A and C. The answer is B. Your Turn: Answer Practice Test #15.

Divide each side by -12. Simplify. Subtract 36 from each side. Substitute a = 3 and b = -6 Simplify. The answer is B.

Steps: Identify a, b, and c. Write the quadratic formula. Substitute the values of a, b, and c. Simplify. The answer is D. Alternative Method: Work Backwards

Solution: Since you are to compare the maximum value of each function, you need to find each function’s vertex. The maximum is the y-coordinate of the vertex. The answer is D.

Solution: 1. Draw x = -2, the axis of symmetry on the graph. 2. Plot the four points given in the table. 4. Connect the points to sketch the parabola. 5. Find the intervals where the x- intercepts are located. The answer is A. 3. Use symmetry to locate three other points.

HOMEWORK: Study the notes, formulas and strategies that you need to solve each problem exercise on Test 2. Remember, notes, formulas and calculators will not be allowed. This review material is posted in my.ccsd.net. Be sure to try answering all the problems here and also the ones in your Practice Test. Prepare well so you can ace this test.