1. 9-1 Quadratic Graphs and Their Properties Graph y = ax2 + c

2. Vocabulary
A quadratic function is a nonlinear (not a line) function that can be written in the standard form y = ax2+ bx + c where a ≠ 0
Every quadratic function has a U-shaped graph called a parabola.

3. Vocabulary
The most basic quadratic function in the family of quadratic functions, called the parent quadratic function, is y = x2 X -2 -1 1 2
Y = 4

4. Parts of a Parabola
The lowest or highest point on a parabola is the vertex.
The line that passes through the vertex and divides the parabola into two symmetric parts is called the axis of symmetry.

5. How does the coefficient a effect the graph?
Graph y = ax2
How does the coefficient a effect the graph?
If “a” is positive (a > 0) then the graph opens up.
If “a” is negative (a < 0) then the graph flips upside down or it opens down.
(Or as I like to call it…makes a SAD face)

6. Graph y = ax2 How does the coefficient a effect the graph?
a can stretch or compress the parabola.
If |a| > 1, then graph is stretched.
(i.e. y = 2x2, y = -3.5x2 , )
If |a| < 1, then the graph is compressed.
( i.e , , )

7. Example 1:
Graph y = 2x2. Compare the graph with the parent function, y = x2.
You need to make a table of values. X -2 -1 1 2
Y =

9. You Try:
Graph y = 1/2x2. Compare the graph with the parent function, y = x2. X -2 -1 1 2
Y =

10. Example 2:
Graph y = -3x2. Compare the graph with the parent function, y = x2.
You need to make a table of values. X -2 -1 1 2
Y =

12. Graph y = ax2 + c The constant “c” moves the graph up or down.
If “c” is positive (c > 0) it moves the graph up.
if “c” is negative (c < 0) it moves the graph down.

13. Example 4:
Graph y = x Compare the graph with the parent function, y = x2.
You need to make a table of values. X -2 -1 1 2
Y =

15. You Try:
Graph y = x2 – 4. Compare the graph with the parent function, y = x2.

17. Homework:
Book: 9.1 p.550 #13-22, 33-36, 47, 58-63