Module 2 Review. Put each equation into factored form. 1. y = x 2 + 4x – 12 2. y = x 2 – 4x – 12 3. y = x 2 + 8x + 12 4. y = x 2 – 8x + 12.

Slides:



Advertisements
Similar presentations
5-3 Transforming parabolas
Advertisements

Essential Question(s): How can you tell if a quadratic function a) opens up or down b) has a minimum or maximum, and c) how many x-intercepts it has?
ParabolasParabolas by Dr. Carol A. Marinas. Transformation Shifts Tell me the following information about: f(x) = (x – 4) 2 – 3  What shape is the graph?
Quadratic Functions, Quadratic Expressions, Quadratic Equations
Section 7.5 – Graphing Quadratic Functions Using Properties.
What is the slope? undefined. What is the slope? m = -1.
Quadratic Functions Review / Warm up. f(x) = ax^2 + bx + c. In this form when: a>0 graph opens up a 0 Graph has 2 x-intercepts.
Unit #3: Quadratics 5-3: Translating Parabolas
EXAMPLE 4 Choose a solution method Tell what method you would use to solve the quadratic equation. Explain your choice(s). a. 10x 2 – 7 = 0 SOLUTION a.
Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?
Solve Using Best Method
Characteristics of a Parabola in Standard Form. Quadratic Vocabulary Parabola: The graph of a quadratic equation. x-intercept: The value of x when y=0.
Graphing Quadratic Functions and Transformations.
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.
Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.
Quadratic Functions & Models How Gravity Has Made the Parabola an Important Graph.
Getting Ready: Zero Product Property If two numbers multiply together to equal zero, one or both of the numbers must equal zero. ie) m x n = 0  m or n.
Graphing and Solving. a)What do they look like? b)How can you tell a function is quadratic? c)What are some terms associated with quadratic functions?
Find the x and y intercepts of each graph. Then write the equation of the line. x-intercept: y-intercept: Slope: Equation:
Quadratic Functions(3) What is a perfect square. What is a perfect square. How to make and complete the square. How to make and complete the square. Sketching.
Fireworks – Finding Intercepts
WRITING LINEAR EQUATIONS FINDING THE X-INTERCEPT AND Y- INTERCEPT.
9.4 Graphing Quadratics Three Forms
REVIEW FOR QUIZ ALGEBRA 1 CP MS. BATTAGLIA & MR. BALDINO.
Warm-Up Find the vertex, the roots or the y- intercept of the following forms: 1. f(x) = (x-4) f(x) = -2(x-3)(x+4) 3. f(x) = x 2 -2x -15 Answers:
Objective - To use the discriminant to determine the number of real solutions for a quadratic. Quadratic FormulaDiscriminant Used to find the roots of.
Fireworks – From Standard to Vertex Form
 What are the three forms a quadratic equation can be written in? Vertex Standard Factored.
6.3 Logarithmic Functions. Change exponential expression into an equivalent logarithmic expression. Change logarithmic expression into an equivalent.
Graphing Quadratic Equations Standard Form & Vertex Form.
Copyright © Cengage Learning. All rights reserved. 4 Quadratic Functions.
Solving Quadratic Equations
 Graph is a parabola.  Either has a minimum or maximum point.  That point is called a vertex.  Use transformations of previous section on x 2 and -x.
2.3 Quadratic Functions. A quadratic function is a function of the form:
Sketching a Quadratic Graph Students will use equation to find the axis of symmetry, the coordinates of points at which the curve intersects the x-axis,
 Objectives: Solve quadratic equations that cannot be factored by completing the square  Vocabulary: Perfect Square Trinomial- A trinomial of the form.
ANSWER 3. Evaluate the expression. Warm Up for Lesson x 2 when x = 4 ANSWER 128 ANSWER –1 2.–4 + x when x = 9 √ Find the (1)Axis of Symmetry, (2)the.
Quadratic Functions and their Graphs If a graph has an axis of symmetry, then when you fold the graph along this axis, the two halves of the graph coincide.
THE SLIDES ARE TIMED! KEEP WORKING! YOUR WORK IS YOUR OWN! Quadratic Systems Activity You completed one in class… complete two more for homework.
Q1: Student has difficulty starting You are given two pieces of information. Which form of a quadratic equation can you match the information to? Q2: Student.
Roots, Zeroes, and Solutions For Quadratics Day 2.
Chapter 6-1 Graphing Quadratic Functions. Which of the following are quadratic functions?
5.3 Again! Warm-up (IN) Learning Objective: To use factoring to solve quadratic equations. Factor:
11-2 Solving Quadratic Equations By Graphing
SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.
5.2 Polynomials, Linear Factors, and Zeros P
SOLVING QUADRATICS DAY 3 (IN THE CALCULATOR) EQ: How can points of intersection be used to solve any equation?
2.3 Factor Standard Equations into X-intercept Form.
Unit 9 Review Find the equation of the axis of symmetry, along with the coordinates of the vertex of the graph and the y-intercept, for the following equation.
6.1 Graphing Quadratic Functions in Standard Form.
Unit 3-1: Graphing Quadratic Functions Learning Target: I will graph a quadratic equation and label its key features.
 What are the three forms a quadratic equation can be written in? Vertex Standard Factored.
Warm Up Important Properties: 1.The graph will open up if ‘a’ ___ 0 and down if ‘a’ ___ 0 3.The vertex formula for: vertex format is: standard format is:
Section 8.7 More About Quadratic Function Graphs  Completing the Square  Finding Intercepts 8.71.
Unit 3. Day 10 Practice Graph Using Intercepts.  Find the x-intercept and the y-intercept of the graph of the equation. x + 3y = 15 Question 1:
Standard Form Objective: To graph the equation of a line in Standard Form from give information. Warm – up: Write the following equations in Standard Form.
Big Idea: -Graph quadratic functions. -Demonstrate and explain the effect that changing a coefficient has on the graph. 5-2 Properties of Parabolas.
Do Now: Solve the equation in the complex number system.
Interpreting Various Forms of Quadratic Equations (2.1.2) October 2nd, 2015.
Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC.
GRAPH QUADRATIC FUNCTIONS. FIND AND INTERPRET THE MAXIMUM AND MINIMUM VALUES OF A QUADRATIC FUNCTION. 5.1 Graphing Quadratic Functions.
1. Whether the parabola opens up or down. 2. The y-intercept. 3. The axis of symmetry 4. The vertex 5. The max/min value 6. The x-intercept(s) Then sketch.
$$$ DEAL OR NO DEAL $$$.
Creating and Graphing Equations Using Vertex Form
What are the equations of the following lines?
Creating & Graphing Quadratic Functions Using Standard Form (3.3.1)
4.4 Different Forms of Quadratic Expressions
I will write a quadratic function in vertex form.
Use the Chain Rule to find {image} where t = 5, u = 3, v = 0. {image}
Presentation transcript:

Module 2 Review

Put each equation into factored form. 1. y = x 2 + 4x – y = x 2 – 4x – y = x 2 + 8x y = x 2 – 8x + 12

Put each equation into vertex form. 1. y = x 2 + 4x – y = x 2 – 4x – y = x 2 + 8x y = x 2 – 8x + 12

Which is the correct factored form of y = x 2 + 5x - 14 a. y = (x + 2)(x – 7) b. y = (x – 2)(x – 7) c. y = (x – 2)(x + 7) d. y = (2x + 5)(x + 7)

Which expression is NOT equivalent to y = 2(x – 1)(x – 3) a. y = (x – 1)(2x – 6) b. y = (2x – 2)(x – 3) c. y = (1/2x – ½)(1/2x – 3/2) d. y = 2x 2 – 8x + 6

Where is the vertex of the equation y = x 2 – 10x + 16 a. (-2, -8) b. (5, -9) c. (3, -13) d. (-5, 9)

Using the equation y = (x – 3)(x + 5), find the following information: a. Standard Form of the equation: a. y-intercept: a. x-intercept:

Using the equation y = (x – 1) 2 – 4, find the following information. a. What form is the given equation written in? b. Vertex: c. Factored Form of the equation:

Write a quadratic equation in each form that has a vertex of (-4, -4) where the vertex is a minimum a. Vertex Form Equation: b. Standard Form Equation: c. Factored Form Equation:

Give an example of a vertex form equation, tell me what is the easiest thing to find from vertex form and explain how you’d find it. Equation: ______ Easy to find: ______ Explain how you’d find it:

Give an example of a standard form equation, tell me what is the easiest thing to find from standard form and explain how you’d find it. Equation: _________ Easy to find: _________ How are you going to find it?

Give an example of a factored form equation, tell me what is the easiest thing to find from factored form and explain how you’d find it. Equation: ________ Easy to find: ________ How are you going to find it?