Download - Graphs of Quadratic Equations
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)