1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
For each function, find the value of y for x = 0, x = 4, and x = –5.
1. y = 6x – 3
2. y = 3.8x – 12
3. y = 1.6x + 5.9
–3, 21, –33
–12, 3.2, –31
5.9, 12.3, –2.1

3. Standards California AF3.1 Graph functions of the form
y = nx2 and y = nx3 and use in solving problems.
California
Standards

4. Vocabulary
quadratic function
parabola

5. A quadratic function is a function in which the greatest power of the variable is 2. The most basic quadratic function is y = nx2 where n ≠ 0.
The graphs of all quadratic functions have the same basic shape, called a parabola.

6. Additional Example 1: Graphing Quadratic Functions
Create a table for each quadratic function, and use it to graph the function.
A. y = x2 + 1
Plot the points and connect them with a smooth curve. x
x y –2 –1 1 2
(–2)
(–1)
(0)
(1)
(2)

7. Additional Example 1: Graphing Quadratic Functions
Plot the points and connect them with a smooth curve.
B. y = x2 – x + 1 x
x2 – x y –2 –1 1 2
(–2)2 – (–2)
(–1)2 – (–1)
(0)2 – (0)
(1)2 – (1)
(2)2 – (2)

8. Check It Out! Example 1
Create a table for each quadratic function, and use it to make a graph.
A. y = x2 – 1
Plot the points and connect them with a smooth curve. x
x2 – y –2 –1 1 2
(–2)2 –
(–1)2 –
(0)2 – –1
(1)2 –
(2)2 –

9. Plot the points and connect them with a smooth curve.
Check It Out! Example 1
Plot the points and connect them with a smooth curve.
B. y = x2 + x + 1 x
x2 + x y –2 –1 1 2
(–2)2 + (–2)
(–1)2 + (–1)
(0)2 + (0)
(1)2 + (1)
(2)2 + (2)

10. Additional Example 2: Application
A reflecting surface of a television antenna was formed by rotating the parabola y = 0.1x2 about its axis of symmetry. If the antenna has a diameter of 4 feet, about how much higher are the sides than the center?

11. Additional Example 2 Continued
First, create a table of values. Then graph the cross section.
y = 0.1x2 y
The center of the antenna is at x = 0 and the height is 0 ft. If the diameter of the mirror is 4 ft, the highest point on the sides are at x = 2 and x = –2.
The height of the sides at x = 0.1(2)2 = 0.4 ft. The sides are 0.4 ft higher than the center.

12. Check It Out! Example 2
A reflecting surface of a radio antenna was formed by rotating the parabola
y = x2 – x + 2 about its axis of symmetry. If the antenna has a diameter of 3 feet, about how much higher are the sides than the center?

13. Check It Out! Example 2 Continued
First, create a table of values and graph the cross section.
3 ft. x
x2 – x y -1 1 2
(–1)2 – (–1)
(0)2 – (0)
(1)2 – (1)
(2)2 – (2)
The center of the antenna is at x = 0
and the height is 2 ft. If the diameter
of the antenna is 3 ft, the highest point on the sides are at x = 2.
The height of the antenna at x = (2)2 – (2) + 2 = 4 ft – 2 ft = 2 ft. The sides are 2 ft higher than the center.

14. Lesson Quiz: Part I
Create a table for the quadratic function, and use it to make a graph.
1. y = x2 – 2

15. Lesson Quiz: Part II
Create a table for each quadratic function, and use it to make a graph.
2. y = x2 + x – 6

16. Lesson Quiz: Part III
3. The function y = 40t – 5t2 gives the height of an arrow in meters t seconds after it is shot upward. What is the height of the arrow after 5 seconds?
75 m