Review for Mastery 8-3 Graphing Quadratic Functions continued - PC\|MAC

Name ________________________________________ Date __________________ Class__________________

LESSON Review for Mastery

8-3 Graphing Quadratic Functions

You can use the axis of symmetry, vertex, and y-intercept to graph a quadratic function.

Graph y = x2 + 6x + 8.

Step 3: Find the y-intercept.

y = (0)2 + 6(0) + 8 y = 8

Substitute 0 for x in the original equation. Simplify.

Step 1: Find the axis of symmetry.

x = - 6 = -3 2(1)

Use

x

=

-

b 2a

Graph the axis of symmetry, x = -3.

Step 2: Find the vertex.

y = (-3)2 + 6(-3) + 8

Substitute -3 for x.

y = 9 - 18 + 8 y = -1

Simplify.

Graph (0, 8). Step 4: Choose two x-values on the same side of the axis of symmetry as the point containing the y-intercept.

Use -2 and -1. y = (-2)2 + 6 (-2) + 8 = 0 Graph (-2, 0). y = (-1)2 + 6 (-1) + 8 = 3 Graph (-1, 3).

Step 5: Reflect those points and connect them with a smooth curve.

Graph the vertex, (-3, -1).

1) axis of symmetry

3) y-intercept

2) vertex

Graph x2 + 4x - 12 by completing the following.

1. Find and graph the axis of symmetry.

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2. Find and graph the vertex.

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3. Find and graph the y-intercept.

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4. Find and graph two more points.

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5. Reflect the points and draw the graph.

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Holt McDougal Algebra 1

Name ________________________________________ Date __________________ Class__________________

LESSON Review for Mastery

8-3 Graphing Quadratic Functions continued

Many real life situations involve quadratic functions. It is important to interpret the graphs correctly. The height in feet of a soccer ball kicked in the air can be modeled by the function f(t) = -16t2 + 32t. Find the ball's maximum height and the time it takes the ball to reach this height. Then find how long the ball is in the air. The graph shows the approximate height of the soccer ball after t seconds. The x-axis is time t in seconds. The y-axis is the height h in feet.

The vertex is the maximum height. 16 feet is the height at 1 second.

The height at 0 seconds is 0 feet.

The height at 2 seconds is 0 feet.

2 seconds is the length of time the ball is in the air. The maximum height is 16 feet. It takes the ball 1 second to reach this height. The soccer ball is in the air for 2 seconds.

The height in feet of a rocket launched straight up in the air can be modeled by the function f(t) = -16t2 + 96t. The graph is shown.

6. Find the time it takes the rocket to reach the maximum height.

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7. Find the rocket's maximum height.

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8. Find how long the rocket was in the air.

____________________________________

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

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Holt McDougal Algebra 1

3. 18 feet; 1.5 seconds; 3 seconds

3.

Practice C 1.

2.

4. 5. 18 feet; 1 second; 2.5 seconds

Review for Mastery 1. x = -2 3. (0, -12)

4. Possible answers: (-1, -15); (1, -7)

2. (-2, -16)

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

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Holt McDougal Algebra 1

5.

2.

6. 3 seconds 8. 6 seconds

7. 144 feet

Challenge

1. 21; 11; 5; 3; 5; 11; 21

3.18; 3.08; 3.02; 3.00; 3.02; 3.08; 3.18

2. (2, 3)

3. x = 2

4. 2

5. -2.27; -2.12; -2.03; -2.00; -2.03; -2.12; -2.27

6. (-1, -2)

7. x = -1

8. -1

9. a. An equation for the axis of symmetry of

the graph of y = ax2

+ bx + c is x =

-b 2a

.

b. One approach is to use graphs, and a second approach is to use tables as in Exercises 1 and 5.

Problem Solving 1.

36 ft; 1.5 seconds 3. H 5. C

4. C

Reading Strategies

1. x = -3; (-3, -4); (0, 5); Possible answers: (-2, -3) and (-1, 0)

2. x = 0; (0, 6); (0, 6); Possible answers: (-2, 4) and (-4, -2)

4 seconds

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Holt McDougal Algebra 1

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