Holt CA Course 1

7-4 Graphing Quadratic Functions

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Holt CA Course 1

7-4 Graphing Quadratic Functions

Warm UpFor 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

Holt CA Course 1

7-4 Graphing Quadratic Functions

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

California Standards

Holt CA Course 1

7-4 Graphing Quadratic Functions

Vocabulary

quadratic functionparabola

Holt CA Course 1

7-4 Graphing Quadratic Functions

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.

Holt CA Course 1

7-4 Graphing Quadratic Functions

Create a table for each quadratic function, and use it to graph the function.

A. y = x2 + 1

Additional Example 1: Graphing Quadratic Functions

Plot the points and connect them with a smooth curve.

x x2 + 1 y

–2

–1

0

1

2

(–2)2 + 1 5

(–1)2 + 1 2

(0)2 + 1 1

(1)2 + 1 2

(2)2 + 1 5

Holt CA Course 1

7-4 Graphing Quadratic Functions

B. y = x2 – x + 1

Additional Example 1: Graphing Quadratic Functions

Plot the points and connect them with a smooth curve.

x x2 – x + 1 y

–2

–1

0

1

2

(–2)2 – (–2) + 1 7

(–1)2 – (–1) + 1 3

(0)2 – (0) + 1 1

(1)2 – (1) + 1 1

(2)2 – (2) + 1 3

Holt CA Course 1

7-4 Graphing Quadratic Functions

A. y = x2 – 1

Check It Out! Example 1

Plot the points and connect them with a smooth curve.

x x2 – 1 y

–2

–1

0

1

2

(–2)2 – 1 3

(–1)2 – 1 0

(0)2 – 1 –1

(1)2 – 1 0

(2)2 – 1 3

Create a table for each quadratic function, and use it to make a graph.

Holt CA Course 1

7-4 Graphing Quadratic Functions

B. y = x2 + x + 1

Check It Out! Example 1

Plot the points and connect them with a smooth curve.

x x2 + x + 1 y

–2

–1

0

1

2

(–2)2 + (–2) + 1 3

(–1)2 + (–1) + 1 1

(0)2 + (0) + 1 1

(1)2 + (1) + 1 3

(2)2 + (2) + 1 7

Holt CA Course 1

7-4 Graphing Quadratic Functions

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?

Additional Example 2: Application

Holt CA Course 1

7-4 Graphing Quadratic FunctionsAdditional Example 2 Continued

First, create a table of values. Then graph the cross section.

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.

y = 0.1x2 y

The height of the sides at x = 0.1(2)2 = 0.4 ft. The sides are 0.4 ft higher than the center.

Holt CA Course 1

7-4 Graphing Quadratic Functions

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?

Check It Out! Example 2

Holt CA Course 1

7-4 Graphing Quadratic FunctionsCheck It Out! Example 2 Continued

x x2 – x + 2 y

-1

0

1

2

(–1)2 – (–1) + 2 4

(0)2 – (0) + 2 2

(1)2 – (1) + 2 2

(2)2 – (2) + 2 4

First, create a table of values and graph the cross section.

3 ft.

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.

Holt CA Course 1

7-4 Graphing Quadratic FunctionsLesson Quiz: Part I

Create a table for the quadratic function, and use it to make a graph.

1. y = x2 – 2

Holt CA Course 1

7-4 Graphing Quadratic FunctionsLesson Quiz: Part II

Create a table for each quadratic function, and use it to make a graph.

2. y = x2 + x – 6

Holt CA Course 1

7-4 Graphing Quadratic Functions

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