Download presentation

Presentation is loading. Please wait.

Published byLuis Ritchie Modified over 5 years ago

1
**3.2 Graphing Quadratic Functions in Vertex or Intercept Form**

Definitions 3 Forms Graphing in vertex form Examples Changing between eqn. forms

2
Quadratic Function A function of the form y=ax2+bx+c where a≠0 making a u-shaped graph called a parabola. Example quadratic equation:

3
**Vertex- Axis of symmetry- The lowest or highest point of a parabola.**

The vertical line through the vertex of the parabola. Axis of Symmetry

4
**Vertex Form Equation y=a(x-h)2+k If a is positive, parabola opens up**

If a is negative, parabola opens down. The vertex is the point (h,k). The axis of symmetry is the vertical line x=h.

5
**Vertex Form (x – h)2 + k – vertex form**

Each function we just looked at can be written in the form (x – h)2 + k, where (h , k) is the vertex of the parabola, and x = h is its axis of symmetry. (x – h)2 + k – vertex form Equation Vertex Axis of Symmetry y = x2 or y = (x – 0)2 + 0 (0 , 0) x = 0 y = x2 + 2 or y = (x – 0)2 + 2 (0 , 2) y = (x – 3)2 or y = (x – 3)2 + 0 (3 , 0) x = 3

6
**Analyze y = (x + 2)2 + 1. Example 1: Graph**

Step 1 Plot the vertex (-2 , 1) Step 2 Draw the axis of symmetry, x = -2. Step 3 Find and plot two points on one side , such as (-1, 2) and (0 , 5). Step 4 Use symmetry to complete the graph, or find two points on the left side of the vertex.

7
Your Turn! Analyze and Graph: y = (x + 4)2 - 3. (-4,-3)

8
**Example 2: Graph y=-.5(x+3)2+4**

a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Table of values x y -1 2 -3 4 -5 2 Vertex (-3,4) (-4,3.5) (-2,3.5) (-5,2) (-1,2) x=-3

9
**Table of values with 5 points?**

Now you try one! y=2(x-1)2+3 Open up or down? Vertex? Axis of symmetry? Table of values with 5 points?

10
(-1, 11) (3,11) X = 1 (0,5) (2,5) (1,3)

11
**Changing from vertex or intercepts form to standard form**

The key is to follow ORDER OF OPERATIONS Ex: y=-(x+4)(x-9) Ex: y=3(x-1)2+8 =-(x2-9x+4x-36) =3(x-1)(x-1)+8 =-(x2-5x-36) =3(x2-x-x+1)+8 y=-x2+5x =3(x2-2x+1)+8 =3x2-6x+3+8 y=3x2-6x+11

12
**Changing from vertex or intercepts form to standard form**

Practice: 1: y = 3(x-4)(x+2) 2: y = -2(x-3)2 - 5

13
Challenge Problem Write the equation of the graph in vertex form.

14
Practice Workbook Page 68 #16-21

15
Assignment Book Page 66 #25-33 and Page 68 #27, 28

Similar presentations

OK

Precalculus Section 1.7 Define and graph quadratic functions

Precalculus Section 1.7 Define and graph quadratic functions

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google