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

Jeff Bivin -- LZHS Quadratic Equations. Jeff Bivin -- LZHS Convert to Standard Form f(x) = 5x 2 - 40x + 46 f(x) = 5(x 2 - 8x + (-4) 2 ) + 46 - 60 f(x)

Jeff Bivin -- LZHS Quadratic Equations. Jeff Bivin -- LZHS Convert to Standard Form f(x) = 5x 2 - 40x + 46 f(x) = 5(x 2 - 8x + (-4) 2 ) + 46 - 60 f(x)

© 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