1. 4.1 Graphing Quadratic Functions
Alg. II

2. Quadratic Function
A function of the form y=ax2+bx+c where a≠0 making a u-shaped graph called a parabola.
Example quadratic equation:

3. Vertex- Axis of symmetry- The lowest or highest point of a parabola.
The vertical line through the vertex of the parabola.
Min. or Max.
Axis of
Symmetry

4. Standard Form Equation
y=ax2 + bx + c
If a is positive, u opens up
If a is negative, u opens down
The x-coordinate of the vertex is at
To find the y-coordinate of the vertex, plug the x-coordinate into the given eqn.
The axis of symmetry is the vertical line x=
Choose 2 x-values on either side of the vertex x-coordinate. Use the eqn to find the corresponding y-values.
Graph and label the 5 points and axis of symmetry on a coordinate plane. Connect the points with a smooth curve.

5. Example 1: Graph y=2x2-8x+6 Axis of symmetry is the vertical line x=2
Table of values for other points: x y
0 6
1 0
2 -2 Min. or Max?
3 0
4 6
* Graph!
a=2 Since a is positive the parabola will open up.
Vertex: use
b=-8 and a=2
Vertex is: (2,-2)
x=2

6. Now you try one. y=-x2+x+12. Open up or down. Vertex. (1/2 , 12 ¼)
Now you try one! y=-x2+x+12 * Open up or down? * Vertex? (1/2 , 12 ¼) * Axis of symmetry? x=1/2 * Table of values with 5 points? Is vertex Min. or Max.? x y -1 10 12
1/2
12 1/4 1 2

7. Assignment