Graphing in Vertex Form and Intercept Form.  What kind of functions are the following…?

Slides:

Advertisements

Similar presentations

5.2 Properties of Parabolas

Advertisements

EXAMPLE 1 Graph y= ax 2 where a > 1 STEP 1 Make a table of values for y = 3x 2 x– 2– 1012 y12303 Plot the points from the table. STEP 2.

The Graph of a Quadratic Function

5.1 GRAPHING QUADRATIC FUNCTIONS I can graph quadratic functions in standard form. I can graph quadratic functions in vertex form. I can graph quadratic.

Chapter 5 – Quadratic Functions and Factoring

4.2: Graphs of Quadratic Functions in Vertex or Intercept Form

EXAMPLE 3 Graph a quadratic function in intercept form

3.2 Intercepts. Intercepts X-intercept is the x- coordinate of a point when the graph cuts the x-axis Y-intercept is the y- coordinate of a point when.

EXAMPLE 1 Graph an equation of a parabola SOLUTION STEP 1 Rewrite the equation in standard form x = – Write original equation Graph x = – y.

Graph an equation of a parabola

Section 4.1: Vertex Form LEARNING TARGET: I WILL GRAPH A PARABOLA USING VERTEX FORM.

EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x x – 7. a. Find the axis of symmetry of the graph of the function.

Table of Contents Graphing Quadratic Functions – Concept A simple quadratic function is given by The graph of a quadratic function in called a parabola.

1 Introduction to Chapter 5 Chapter 5 – Quadratic Functions 1. Four ways to solve them 2. How to graph quadratic functions and inequalities Remember! Bring.

Activity 4.2 The Shot Put.

Goal: Graph quadratic functions in different forms.

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.

5.1: Graphing Quadratic Functions

Warm Up Tuesday, 8/11 Describe the transformation, then graph the function. 1) h(x)= (x + 9) ) g(x) = -5x Write the resulting equation.

Graphing Quadratic Equations Standard Form & Vertex Form.

Parabolas Our Fourth Conic Form (9.5). POD What other conic forms have we looked at? Why do we call them conic forms? What’s the primary skill we’ve used.

Warm Up #2 Find the Product: a. (x – 5)2 b. 4(x +5)(x – 5) ANSWER

PARABOLAS GOAL: GRAPH AND EQUATIONS OF PARABOLAS.

2.3 Quadratic Functions. A quadratic function is a function of the form:

G RAPHING A Q UADRATIC F UNCTION A quadratic function has the form y = ax 2 + bx + c where a  0.

Graphing Quadratic Functions A “Shortcut” and A “Summary”

Unit 1: Function Families Lesson 5: Transformations & Symmetry Notes Graph y = ax 2 + bx + c.

4.1 Graph Quadratic Functions in Standard Form

Introduction The equation of a quadratic function can be written in several different forms. We have practiced using the standard form of a quadratic function.

5 – 1: Graphing Quadratic Functions (Day 1 ) Objective: CA 10: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.

EXAMPLE 3 Graph a function of the form y = ax 2 + bx + c Graph y = 2x 2 – 8x + 6. SOLUTION Identify the coefficients of the function. The coefficients.

Vertex form Form: Just like absolute value graphs, you will translate the parent function h is positive, shift right; h is negative, shift left K is positive,

5.3 Transformations of Parabolas Goal : Write a quadratic in Vertex Form and use graphing transformations to easily graph a parabola.

Creating and Graphing Equations Using the x - intercepts Adapted from Walch Education.

Section 8.7 More About Quadratic Function Graphs  Completing the Square  Finding Intercepts 8.71.

Warm Up Lesson 4.1 Find the x-intercept and y-intercept

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic.

1.7 Graphing Quadratic Functions. 1. Find the x-intercept(s). The x-intercepts occur when Solve by: Factoring Completing the Square Quadratic Formula.

Big Idea: -Graph quadratic functions. -Demonstrate and explain the effect that changing a coefficient has on the graph. 5-2 Properties of Parabolas.

WARM-UP: Graphing Using a Table x y = 3x  2 y -2 y = 3(-2)  2 -8 y = 3(-1)  y = 3(0)  y = 3(1)  y = 3(2)  2 4 GRAPH. y = 3x 

How does the value of a affect the graphs?

G RAPHING A Q UADRATIC F UNCTION A quadratic function has the form y = ax 2 + bx + c where a  0. The graph is “U-shaped” and is called a parabola. The.

Graphing Quadratics in Vertex and Intercept Form Vertex Form y = a(x – h) 2 + k Intercept Form y = a(x – p)(x – q)

Objectives: Be able to graph a quadratic function in vertex form Be able to write a quadratic function in vertex form (2 ways)

Unit 2 – Quadratic Functions & Equations. A quadratic function can be written in the form f(x) = ax 2 + bx + c where a, b, and c are real numbers and.

Warm-Up Exercises 1. Identify the axis of symmetry for the graph of y = 3x 2. ANSWER x = 0 2. Identify the vertex of the graph of y = 3x 2. ANSWER (0,

Do Now Find the value of y when x = -1, 0, and 2. y = x2 + 3x – 2

y = ax 2 + bx + c where a  0. GRAPHING A QUADRATIC FUNCTION

Algebra Lesson 10-2: Graph y = ax2 + bx + c

3.3 Quadratic Functions Quadratic Function: 2nd degree polynomial

Objectives Transform quadratic functions.

3.2 Graphing Quadratic Functions in Vertex or Intercept Form

Graphing Quadratic Functions in Vertex or Intercept Form

parabola up down vertex Graph Quadratic Equations axis of symmetry

Lesson 5.3 Transforming Parabolas

What is the x-intercept?

4.10 Write Quadratic Functions and Models

8.4 - Graphing f (x) = a(x − h)2 + k

Homework Questions.

Daily Check Factor: 3x2 + 10x + 8 Factor and Solve: 2x2 - 7x + 3 = 0.

Drawing Graphs The parabola x Example y

Section 10.2 “Graph y = ax² + bx + c”

Graphing Quadratic Functions

Graphing f(x) = (x - h) + k 3.3A 2 Chapter 3 Quadratic Functions

Section 8.1 “Graph y = ax²”.

9-3 Graphing y = ax + bx + c up 1a. y = x - 1 for -3<x<3

Presentation transcript:

Graphing in Vertex Form and Intercept Form

 What kind of functions are the following…?

  y = a(x – h) 2 + k  It is the graph of the parabola y = ax 2 translated horizontally h units and vertically k units.  The vertex is (h, k)  The axis of symmetry is x = h. Vertex Form

  1. Identify the vertex and plot it.  Ex: y = 3(x – 5) 2 – 8  Vertex: (5, -8)  Ex: y = -½ (x + 2)  Vertex: (-2, 4)  Ex: y = (x + 7) 2 – 1  Vertex: (-7, -1)  2. Draw the line of symmetry through the vertex.  3. Evaluate the function for values of x near the line of symmetry and plot those points. Graphing in vertex form

  Graph: y = ½(x – 3) Example

  Use the calculator to graph. Notice anything?  y = 2(x – 3)(x + 6)  y = x(x + 4)  y = (x – 5)(x – 1)  If you know the x intercepts, you can plot them to help make your graph.  The vertex will have an x-value that is halfway between the x-intercepts. Intercept form

  y = a(x – p)(x – q)  The x-intercepts are p and q.  The axis of symmetry is halfway between (p, 0) and (q, 0).  The graph opens up if a is positive.  Example: graph y = -x(x – 4) Intercept form