1. Do Now 3/18/19

2. Punchline worksheet 14.2

3. Essential Question What are some characteristics of the graph of a quadratic function of the form f(x) = ax2?
With your partner, complete Exploration 1 on pages in your Student Journal

4. Chapter 8 “Graphing Quadratic Functions”
(8.1) Graphing f(x) = ax²
(8.2) Graphing f(x) = ax² + c
(8.3) Graphing f(x) = ax² + bx + c
(8.4) Graphing f(x) = a(x - h)² + k
(8.5) Using Intercept Form
(8.6) Comparing Linear, Exponential, and Quadratic Functions

5. Learning Goal Learning Target SWBAT graph quadratic functions
SWBAT graph functions of the form f(x) = ax² and f(x) = ax² + c

6. Section 8.1 “Graphing f(x) = ax²”
Quadratic Function
A nonlinear function that can be written in the standard form f(x) = ax² + bx + c where a = 0.
The graph of a quadratic function is in the form of a U-shape and called a parabola.

7. Graphing: f(x) = ax² y-axis f(x) = x² x-axis Vertex- Axis of Symmetry-
“Parent
Quadratic
Function” x y 1 1 2 4 3 9 -1 1 -2 4
x-axis -3 9
Vertex-
the lowest or
highest point of the parabola
Axis of Symmetry-
the line that divides a
parabola into 2 symmetric parts

8. Identifying Characteristics of Quadratic Functions
Vertex:
(-1, -2)
Axis of Symmetry:
x = -1
Domain:
All real numbers
Range:
y ≥ -2

9. Identify the Characteristics of Quadratic Functions
On Your Own
Identify the Characteristics of Quadratic Functions

10. Graphing: y = ax² y = 3x² x-axis y-axis x y 1 3 2 12 -1 3 -2 12
“Parent Quadratic
Function” y = x² x y 1 3 2 12 -1 3 -2 12
How does y = 3x² differ from the parent function y = x²?
x-axis
y-axis

11. Graphing: y = ax² y = -1/4x² x-axis y-axis x y 1 -1/4 2 -1 4 -4 6 -9
“Parent Quadratic
Function” y = x²
y = -1/4x² x y
x-axis 1
-1/4 2 -1 4 -4 6 -9 -1
-1/4 -2 -1 -4 -4
y-axis -6 -9
y = -1/4x²

12. Graph the Following Functions
On Your Own
Graph the Following Functions
g(x) = 5x2
g(x) = -3x2
g(x) = 1/3x2

13. Section 8.2 “Graphing f(x) = ax² + c”

14. Graphing: y = ax² + c x-axis y-axis
“Parent Quadratic
Function” f(x) = x²
g(x) = 3x² -3
Compare to the graph of the parent function f(x) = x2
g(x) = 3x²– 3 x y -3 1 2 9
x-axis -1 -2 9
g(x) is a vertical translation down 3 units and a vertical stretch by a factor of 3
y-axis

15. Graph the Following Functions. Compare to the graph of f(x) = x2.
On Your Own
Graph the Following Functions. Compare to the graph of f(x) = x2.
g(x) = x2 – 5
h(x) = x2 + 3

16. Zeros of a Function
an x-value for which f(x) = 0. A zero of a function is an x-intercept of the graph of the function.
To find the zeros of a function, graph the function and locate the x-intercepts.
f(x) = -12x2 + 3
x = ½ and -½

17. Find the Zeros of the Functions
On Your Own
Find the Zeros of the Functions
y = x2 – 1
f(x) = -x2 + 25
f(x) = 4x2 – 16
x = 1 & -1
x = 5 & -5
x = 2 & -2

18. Homework

19. Punchline worksheet 14.1