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Worksheet Section 10.5 v01
F2009 Math 085
Dressler
Name___________________________________
Determine if the parabola whose equation is given opens
upward or downward.
1) y = x2 - 2x - 9
Graph the parabola whose equation is given.
11) y = x2 + 2x - 8
y
10
5
2) y = -x2 - 2x - 9
-10
-5
3) y = 3x2 - 2x - 5
5
10
x
5
10
x
-5
-10
4) y = -4x2 - 2x + 2
12) y = -x2 - 4x + 5
Find the x-intercepts and the y-intercept for the parabola
whose equation is given. If an intercept is an irrational
number, round it to the nearest tenth.
5) y = x2 - 4
y
10
5
-10
-5
6) y = x2 + 14x
-5
-10
7) y = -x2 + 13x - 42
8) y = 2x2 - 22x + 48
9) y = 2x2 + 28x + 90
10) y = x2 + 4x - 7
1
Use the coordinates of the vertex to solve the problem.
Round your answer to the nearest tenth, if necessary.
16) The cost, in millions of dollars, for a company
to manufacture x thousand automobiles is
given by the function C(x) = 4x2 - 40x + 200.
13) y = x2 - 6x + 8
y
10
5
Find the number of automobiles that must be
produced to minimize cost.
-10
-5
5
10
x
-5
17) The profit that the vendor makes per day by
selling x pretzels is given by the function
P(x) = -0.002x2 + 1.4x - 50. Find the number of
-10
pretzels that must be sold to maximize profit.
14) y = -x2 + 6x - 8
18) A projectile is fired from a cliff 600 feet above
the water. The height h of the projectile above
32x2
the water is given by h = + x + 600,
(120)2
y
10
5
-10
-5
5
10
where x is the horizontal distance of the
projectile from the base of the cliff. Find the
maximum height of the projectile.
x
-5
19) An arrow is fired into the air with an initial
velocity of 64 feet per second. The formula
y = -16x2 + 64x
-10
models the arrow's height above the ground, y,
in feet, x seconds after it was shot into the air.
When does the arrow reach its maximum
height? What is that height?
15) y = x2 + 4
y
10
5
-10
-5
Graph the parabola whose equation is given.
20) y = x2 - 6x
5
10
x
y
10
-5
5
-10
-10
-5
5
-5
-10
2
10
x
21) y = x2 - 2x - 3
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
22) y = -x2 - 2x + 8
y
10
5
-10
-5
-5
-10
3
Answer Key
Testname: WS10.5V01
1) Upward
2) Downward
3) Upward
4) Downward
5) x-intercepts: 2 and -2; y-intercept: -4
6) x-intercepts: 0 and -14; y-intercept: 0
7) x-intercepts: 6 and 7; y-intercept: -42
8) x-intercepts: 8 and 3; y-intercept: 48
9) x-intercepts: -5 and -9; y-intercept: 90
10) x-intercepts: 1.3 and -5.3; y-intercept: -7
11)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
-10
12)
y
10
5
-10
-5
-5
-10
13)
y
10
5
-10
-5
-5
-10
4
Answer Key
Testname: WS10.5V01
14)
y
10
5
-10
-5
5
10
x
5
10
x
10
x
-5
-10
15)
y
10
5
-10
-5
-5
-10
16) 5 thousand automobiles
17) 350 pretzels
18) 712.5 ft
19) 2 seconds; 64 feet
20)
y
10
5
-10
-5
5
-5
-10
5
Answer Key
Testname: WS10.5V01
21)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
22)
y
10
5
-10
-5
-5
-10
6