Download presentation

Presentation is loading. Please wait.

Published bySydney Underwood Modified over 4 years ago

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

Similar presentations

OK

Holt CA Course 1 2-7 Equations in Two Variables Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Holt CA Course 1 2-7 Equations in Two Variables Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google