5-1
____________ PERIOD _____
NAME ______________________________________________ DATE
5-1
Skills Practice
Practice
Graphing Quadratic Functions
Graphing Quadratic Functions
For each quadratic function, find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. 1. f(x) ⫽ 3x2
2. f(x) ⫽ x2 ⫹ 1
3. f(x) ⫽ ⫺x2 ⫹ 6x ⫺ 15
4. f(x) ⫽ 2x2 ⫺ 11
5. f(x) ⫽ x2 ⫺ 10x ⫹ 5
6. f(x) ⫽ ⫺2x2 ⫹ 8x ⫹ 7
0; x ⫽ 0; 0
1; x ⫽ 0; 0
⫺11; x ⫽ 0; 0
Complete parts a–c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function.
⫺15; x ⫽ 3; 3
5; x ⫽ 5; 5
____________ PERIOD _____
1. f(x) ⫽ x2 ⫺ 8x ⫹ 15
2. f(x) ⫽ ⫺x2 ⫺ 4x ⫹ 12
15; x ⫽ 4; 4
7; x ⫽ 2; 2
x
0
2
4
6
8
f (x) 15 3 ⫺1 3 15 16
x
⫺6 ⫺4 ⫺2 0
1; x ⫽ 0.5; 0.5
2
f (x) 0 12 16 12 0
f (x )
f (x ) (–2, 16)
x
⫺1 0 0.5 1
f (x) 5
1 0.5 1
2 5
f(x)
16
12 12 8
8. f(x) ⫽
0; x ⫽ 0; 0 x
⫺2 ⫺1 0
9. f(x) ⫽
4; x ⫽ 2; 2
1
2
2
4
f (x) 16 4
0
4 16
8 4
6
x
0
f (x) 8
f (x )
2
4
3
4
6
0 ⫺1 0
8
f (x )
16
(0, 0)
x
12 8 4 (2, 0) –2
O
2
O 4
6x
x (3, –1)
Determine whether each function has a maximum or a minimum value, and find the maximum or minimum value. Then state the domain and range of the function. 10. f(x) ⫽ 6x2
min.; 0; all reals; {f(x) | f(x) ⱖ 0} 13. f(x) ⫽ x2 ⫹ 2x ⫹ 15
11. f(x) ⫽ ⫺8x2
max.; 0; all reals; {f(x) | f(x) ⱕ 0} 14. f(x) ⫽ ⫺x2 ⫹ 4x ⫺ 1
Glencoe Algebra 2
min.; 14; all reals; {f(x) | f(x) ⱖ 14}
max.; 3; all reals; {f(x) | f(x) ⱕ 3}
16. f(x) ⫽ ⫺2x2 ⫹ 4x ⫺ 3
17. f(x) ⫽ 3x2 ⫹ 12x ⫹ 3
max.; ⫺1; all reals; {f(x) | f(x) ⱕ ⴚ1}
min.; ⫺9; all reals; {f(x) | f(x) ⱖ ⴚ9}
12. f(x) ⫽ x2 ⫹ 2x
min.; ⫺1; all reals; {f(x) | f(x) ⱖ ⴚ1}
15. f(x) ⫽ x2 ⫹ 2x ⫺ 3
min.; ⫺4; all reals; {f(x) | f(x) ⱖ ⴚ4}
18. f(x) ⫽ 2x2 ⫹ 4x ⫹ 1
min.; ⫺1; all reals; {f(x) | f(x) ⱖ ⴚ1}
O
2
4 6 (4, –1)
(0.5, 0.5)
8x –6
–4
–2
O
2x
O
x
Determine whether each function has a maximum or a minimum value, and find the maximum or minimum value of each function. Then state the domain and range of the function. 4. f(x) ⫽ x2 ⫹ 2x ⫺ 8
min.; ⫺9; all reals; {f(x) | f(x) ⱖ ⴚ9}
7. f(x) ⫽ 2x2 ⫹ 4x ⫺ 6
min.; ⫺8; all reals; {f(x) | f(x) ⱖ ⴚ8}
5. f(x) ⫽ x2 ⫺ 6x ⫹ 14
6. v(x) ⫽ ⫺x2 ⫹ 14x ⫺ 57
min.; 5; all reals; {f(x) | f(x) ⱖ 5}
max.; ⫺8; all reals; {f(x) | f(x) ⱕ ⴚ8}
8. f(x) ⫽ ⫺x2 ⫹ 4x ⫺ 1
9. f(x) ⫽ ⫺ᎏᎏx2 ⫹ 8x ⫺ 24
max.; 3; all reals; {f(x) | f(x) ⱕ 3}
2 3
max.; 0; all reals; {f(x) | f(x) ⱕ 0}
10. GRAVITATION From 4 feet above a swimming pool, Susan throws a ball upward with a velocity of 32 feet per second. The height h(t) of the ball t seconds after Susan throws it is given by h(t) ⫽ ⫺16t2 ⫹ 32t ⫹ 4. Find the maximum height reached by the ball and the time that this height is reached. 20 ft; 1 s 11. HEALTH CLUBS Last year, the SportsTime Athletic Club charged $20 to participate in an aerobics class. Seventy people attended the classes. The club wants to increase the class price this year. They expect to lose one customer for each $1 increase in the price. a. What price should the club charge to maximize the income from the aerobics classes?
$45 b. What is the maximum income the SportsTime Athletic Club can expect to make?
$2025 Chapter 5
8
Glencoe Algebra 2
Chapter 5
Answers
9
Glencoe Algebra 2
(Lesson 5-1)
f (x )
⫺ 6x ⫹ 8
8; x ⫽ 3; 3
⫺2 0
x
x2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A3
f (x) ⫺8 ⫺2 0 ⫺2 ⫺8
O
⫺ 4x ⫹ 4
x2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. f(x) ⫽
⫺2x2
Answers
Complete parts a–c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function.
3. f(x) ⫽ 2x2 ⫺ 2x ⫹ 1
12; x ⫽ ⫺2; ⫺2
Lesson 5-1
Chapter 5
NAME ______________________________________________ DATE
