Download presentation

Presentation is loading. Please wait.

1
**6.6 Analyzing Graphs of Quadratic Functions**

Goal 1: Analyze quadratic functions of the form y=a(x-h)2+k Goal 2: Write a quadratic function in the form y=a(x-h)2+k

2
**Vertex form: y=a(x-h)2+k**

(h,k): the vertex of the parabola x=h: the axis of symmetry Remember: adding inside the ( ) moves the graph to the left subtracting inside the ( ) moves the graph to the right adding outside the ( ) moves the graph up subtracting outside the ( ) moves the graph down multiplying by a whole number outside the ( ) makes the graph narrower multiplying by a fraction outside the ( ) makes the graph narrower

3
**Ex. Analyze. Then draw the graph.**

y=(x+2)2+1 y=a(x-h)2+k y=(x-(-2))2+1 h=-2, k=1 vertex: (-2, 1) Axis of symmetry: x=-2 Opens: Up This graph shifts left 2 places and up 1 place.

4
**Ex. Analyze. Then draw the graph.**

y=(x-3)2+2 y=a(x-h)2+k h=3, k=2 vertex: (3, 2) Axis of symmetry: x=3 Opens: Up This graph shifts right 3 places and up 2 places.

5
**Ex. Write the function in vertex form. Then analyze the function.**

y=x2+8x-5 y=(x2+8x+c)-5-c y=(x2+8x+42)-5-16 y=(x+4)2-21 y=(x-(-4))2+(-21) Vertex: (-4, -21) Sym: x=-4 Opens: up This graph shifts left 4 places and down 21 places.

6
**Ex. Write the function in vertex form. Then analyze the function.**

y=x2+2x+4 y=(x2+2x+c)+4-c y=(x2+2x+12)+4-1 y=(x+1)2+3 y=(x-(-1))2+3 Vertex: (-1, 3) Sym: x=-1 Opens: up This graph shifts left 1 place and up 3 places.

7
**Ex. Write the function in vertex form. Then analyze the function.**

y=-3x2+6x-1 y =(-3x2+6x)-1 y =-3(x2-2x)-1 y =-3(x2-2x+c)-1-(-3)c Y = -3(x2-2x+1)-1-(-3)(1) y =-3(x-1)2-1-(-3)(1) y =-3(x-1)2-1+3 y =-3(x-1)2+2 Vertex: (1, 2) Sym: x=1 Opens: down This graph shifts right 1 place and up 2 places. This graph gets more narrow.

8
**Ex. Write the function in vertex form. Then analyze the function.**

y=-2x2-4x+2 y =(-2x2-4x)+2 y =-2(x2+2x)+2 y =-2(x2+2x+c)+2-(-2)c y =-2(x+1)2+2-(-2)(1) y =-2(x+1)2+2+2 y =-2(x+1)2+4 Vertex: (-1, 4) Sym: x=-1 Opens: down This graph shifts left 1 place and up 4 places. This graph gets wider.

9
**y=a(x-h)2+k (1)=a((2)-(-1))2+(4) 1=a(2+1)2+4 -3=a(3)2 -3=9a -1/3=a**

Ex. Write an equation for the parabola whose vertex is at (-1, 4) and passes through (2, 1). y=a(x-h)2+k (1)=a((2)-(-1))2+(4) 1=a(2+1)2+4 -3=a(3)2 -3=9a -1/3=a y=-1/3(x+1)2+4

10
**y=a(x-h)2+k (4)=a((3)-(1))2+(2) 4=a(3-1)2+2 2=a(2)2 2=4a 1/2=a**

Ex. Write an equation for the parabola whose vertex is at (1, 2) and passes through (3, 4). y=a(x-h)2+k (4)=a((3)-(1))2+(2) 4=a(3-1)2+2 2=a(2)2 2=4a 1/2=a y=1/2(x-1)2+2

Similar presentations

OK

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on brand marketing Ppt on beautiful places in india Ppt on adverbs for grade 2 Ppt on computer malware spyware Ppt on articles for class 7 Ppt on do's and don'ts of group discussion images Ppt on automobile industry in india free download Ppt on law against child marriage Ppt on area related to circle of class 10 Ppt on shell scripting in linux