Quadratic Functions Worksheets With Answer Key - Pre-Calculus, Michigan State University Page 6
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611. You have 300 feet of fencing to enclose four garden plots as shown below. Find the length and width
of the outer dimensions that will maximize the area. What is the largest area that can be enclosed?
12. A rain gutter is made from sheets of aluminum that are 20 inches wide by turning up the edges to
form right angles. Determine the depth of the gutter that will maximize its cross-section area and
allow the greatest amount of water to flow. What is the maximum cross-sectional area?
13. The path of a basketball thrown from the free throw line can be modeled by the quadratic function
2
f
(
x
)
=
−
. 0
06
x
+
1
5 .
x
+
6
, where x is the horizontal distance (in feet) from the free throw line and
f
(x
)
is the height (in feet) of the ball. Find the maximum height of the basketball. If the ball thrown
is an air ball, how far from the free throw line will the ball land? (Round to nearest tenths.)
14. A rocket is shot up vertically from a 10-foot platform. The quadratic function
2
) (
=
−
16
+
256
+
10
models the rocket’s height above the ground,
) (t
, in feet, t seconds after it
h
t
t
t
h
is launched. (Round to nearest tenths.)
(a) How many seconds does it take the rocket to reach its maximum height?
(b) What is its maximum height?
(c) Find h(0).
(d) How long will it take the rocket to hit the ground?
15. The annual yield per apple tree is fairly constant at 320 pounds when the number of trees per acre is
50 or fewer. For each additional tree over 50, the annual yield per tree for all trees on the acre
decreases by 4 pounds due to overcrowding. Find the number of trees that should be planted on an
acre to produce the maximum yield. How many pounds is the maximum yield?
3.2 Homework Answers: 1. c
2. a
3. b
4. d
5. (a) (3, -1); (b) (-1, 5); (c) (2, -5); (d) (2, 7);
3
49
(e)
−
−
; (f) (-2, 9)
6. (a) (1, -4); (b) x = 1; (c) x -intercepts: 1, 3; y- intercept: -3;
,
2
4
(d) D:
(
−∞
,
∞
)
; R:
[
−
, 4
∞
)
7. (a) (-3, 21); (b) x = -3; (c) D:
(
−∞
,
∞
)
; R:
(−∞
,
21
]
;
1
2
2
2
8. (a)
y
=
( 5
x
−
) 1
−
8
; (b)
y
=
−
( 3
x
−
) 5
+
2
9.
33 feet by 50 feet;
1666
square feet
3
3
10. 25 feet by 100 feet; 2500 square feet
11. 50 feet by 50 feet; 2500 square feet
12. 5 inches; 50 square inches
13. 15.38 feet; 28.51 feet
14. (a) 8 seconds; (b) 1034 feet;
(c) 10; (d) 16.04 seconds
15. 65 trees; 16,900 pounds
Page 6 (Section 3.2)
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