Graphs of Quadratic Equations

Standard Form:

y = ax2+bx+ c

Shape: Parabola

Vertex: high or low point

Axis of Symmetry:Line that divides parabola into two

parts that are mirror image of each other.

Axis of Symmetry Verte

x

The vertex has an x-coordinate of

a

bx

2

The axis of symmetry is the vertical line passing through

a

bx

2

y = x2

012

0

2

a

b a

bx

2

First find the vertex.

This is the x value of the vertex, now find the y value. If x = 0, y = 0

Vertex = (0,0)

0 is the axis of symmetry:

Example: y = x2

Make a table for y = x2

x x2 y (x,y)

-1 (-1)2 1 (-1,1)

0 (Vertex) (0)2 0 (0,0)

1 (1)2 1 (1,1)

Since the vertex is (0,0), pick an x value to the right and left of 0.

To graph a Quadratic Equation

y = ax2+bx+c

y = -ax2+bx+cIf a is positive, the parabola opens up

If a is negative, the parabola opens down

Graph Points

Line of symmetry

A is positive 1, so the parabola opens up with (0,0) as the low

point.

GRAPH: y = x2-x-6

• Identify the a, b, and c values

• First find the vertex

• Make a table with an x value to the right and left of the vertex x value

• Graph these points and connect.

• Label the vertex

Find vertex and plug in to find y. value to have high or low point.

1. a

bx

2

12

)1(

2

1

The x value of the vertex is 1/2

• Now find the y value of the vertex by plugging x back into the equation. y = x2-x-6

• y = (1/2)2 – ½ - 6 • The y value is -25/4.• Now pick a point to the left and right

of ½.

GRAPH:y = x2-x-6x x2-x-6 y (x,y)

-2 (-2)2-(-2)-6 0 (-2,0)

0 (0)2-(0)-6 -6 (0,-6)

2 22-2-6 -4 (2,-4)

I try to pick points equal distance from the vertex x value. I also tried 0 here.

Vertex low

Y=x2-x-6

)4

16

,2

1(

2

1

opens up (a positive)

line of symmetry x =

Line of Symmetry a

b

2

)2(2

2

Graph: y= -2x2+2x+1

a is negative-opens down

= 12

Find the y value, then pick a point to the left and right of 1/2 to see how to draw the parabola.

x 2x +2x+1 y (x,y)0 2(0) +2(0)+1 1 (0,1)

2 +2 +11 2(1) +(2)+1 1 (1,1)

- 2

-

- 2

2

2

12- )

2

1( )

2

1(

2

3 )2

3

,2

1(

y=-2x2+2x+1

Use parabola to find the height of a shot put.

Height in feet

Distance in feet

34.15

Vertex is height

Equation: y= -.01464x2+x+5

a

bx

2

)01464.(2

1

02928.

1

15.34

USE CALCULA

TOR!

Put x back in to find y value

y = -.01464(34.15)2+34.15+5

= 22.08 ft. high

(34.15,22.08) vertex (high

point)