Objective: To us the vertex form of a quadratic

equation

5-3 TRANSFORMING PARABOLAS

In the following table the first column is written in standard form. In the second column, each function has been written in vertex form. Use multiplication to verify that the functions in each row are equivalent.

Compare the values of 2b

a and h in each row. Write a formula to show the

relationship between

2

b

a and h

Standard form :

Vertex Form : 2y ax bx c 2( )y a x h k 2

b

a h

2 4 4y x x 2( 2)y x

2 6 8y x x 2( 3) 1y x

23 12 8y x x 23( 2) 4y x

22 12 19y x x 22( 3) 1y x

THE FAMILY OF QUADRATIC FUNCTIONS

Vertical Stretch or Shrink, and/or Reflection in the x-axis

Parent Function:Reflection in x-axis:

Stretch (a>1) or shrink (0<a<1) by factor a:Reflection in x-axis:

Vertex FormThe graph (and vertex) of 2y axshifts h units horizontally and k units vertically.

For h>0, the graph shifts right.For h<0, the graph shifts left.For k>0, the graph shifts up.For k<0, the graph shifts down.

The vertex is (h , k) and the axis of symmetry is the line x = h.

2y x2y x2y ax2y ax

2( )y a x h k

USING VERTEX FORM TO GRAPH A PARABOLA

Graph21

( 2) 32

y x

STEP 1: Identify the vertex ( h, k )

--Graph the vertex and draw the axis of symmetry

STEP 2: Find another point. (Pick a value for x and put into the equation to find y)

Step 3: Use the fact that parabolas are symmetric to plot second point

Step 4: Sketch the curve

Write the equation of the parabola using vertex form.

2( )y a x h k 2( 3) 4y a x

Substitute (5, -4) into this equation to find a24 (5 3) 4

8 4

2

a

a

a

The equation of the parabola is22( 3) 4y x

Use vertex form to write the equation of the parabola