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WorksheetsQuadratic Textual Problems
Total questions: 21
Worksheet time: 1hrs 1mins
Name
Class
Date
1.
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t2 +128t
(if air resistance is neglected). When will the object reach its maximum height?
h(t) = -16t2 +128t
(if air resistance is neglected). When will the object reach its maximum height?
a)
4 ft
b)
0 seconds
c)
0 ft
d)
4 seconds
2.
How high would you jump if the equation for jumping from a cliff is:
h(t) = -16t2 + 8t + 24?
h(t) = -16t2 + 8t + 24?
a)
25
b)
24
c)
8
d)
26
3.
The function
f(t) = -5t2+20t + 60
models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?
f(t) = -5t2+20t + 60
models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?
a)
4 seconds
b)
-2 seconds
c)
6 seconds
d)
9 seconds
4.
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t2 + 64t + 80.
What will be the object's maximum height?
s(t) = –16t2 + 64t + 80.
What will be the object's maximum height?
a)
2 ft
b)
80 ft
c)
144 ft
d)
64 ft
5.
True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing
The solution, root, x-intercept, and zero of a problem are all the same thing
a)
True
b)
False, because the solution and root are the same but the x-intercept and zero are different
c)
False, because the x-intercept and root are the same but the zero and solution are different
d)
False, they are all different
6.
What is the formula for solving for the Axis of Symmetry?
a)
b2-4ac
b)
-b(+ -) Sq Root of b2-4ac/ 2a
c)
b/2a
d)
-b/2a
7.
What are the steps to solve the word problem: What is the maximum height you can reach if you jump off the cliff with the formula: h(t)= -16t2 + 8t +24?
a)
Calculate the AoS as 1/2, plug 1/2 into the equation for t
b)
Calculate using the formula -b/2a
c)
Calculate the AoS as 1/4, plug 1/4 into the equation for t
d)
Factor out -8, then factor the remaining equation, then switch the signs or use the Quad Formula
8.
A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 feet. Use the formula:
h(t) = -16t2+5t+15
How long will it take for the ball to reach its maximum height? What should you find? Write on your paper why.
h(t) = -16t2+5t+15
How long will it take for the ball to reach its maximum height? What should you find? Write on your paper why.
a)
Roots (Solutions)
b)
Axis of Symmetry
c)
Vertex
d)
y-intercept
9.
How fast would you reach the water if you jump of a cliff using the formula: h(t) = -16t2 + 8t + 24?
a)
8
b)
1
c)
1.5
d)
1/4
10.
At what time would you reach 16 ft above the water if you jump of a cliff using the formula:
h = -16t2 + 8t + 24?
h = -16t2 + 8t + 24?
a)
8
b)
1
c)
1/2
d)
1/4
11.
In order to find the vertex of an in standard form, the first two steps are to use the equation _____ to find the axis of symmetry, and then you can plug that value back into the equation to find the _____.
a)
-b/2a, vertex
b)
(x-h)^2, y-intercept
c)
(x-r1), solution
d)
ax^2, vertex
12.
Does the equation open or down?
Y = -3x2 +7x - 2
On your paper, write how you know.
Y = -3x2 +7x - 2
On your paper, write how you know.
a)
up
b)
down
13.
Which equation below is a quadratic? On your paper, explain.
a)
y=9x+5
b)
y=3x2-6
c)
y=5x3+6
d)
x=3x
14.
Does the following quadratic equation have a maximum or minimum value?
y=x²+2x-3
Explain how you know on your paper.
y=x²+2x-3
Explain how you know on your paper.
a)
Minimum value, because the a value is positive
b)
Maximum value, because the b value is positive
c)
Maximum value, because the a value is positive
d)
Minimum value, because the c value is negative
15.
Find the axis of symmetry for
f(x) = 4x2+16x-5
f(x) = 4x2+16x-5
a)
x = 2
b)
x = -2
c)
y = 4
d)
y = 32
16.
Find the vertex of
f(x) = -x2 - 4x + 12.
f(x) = -x2 - 4x + 12.
a)
(-2, 16)
b)
(-2, 14)
c)
(2, 4)
d)
(-2, 4)
17.
What is the vertex? Explain your answer on your paper.
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)
18.
If each mark on the x-axis represents one second, when did the object reach the ground?
a)
2.5 seconds
b)
6 seconds
c)
5.5 seconds
d)
5 seconds
19.
What is the vertex of the parabola: y=2(x-3)2+4.
Explain how you got your answer on paper.
Explain how you got your answer on paper.
a)
(3,4)
b)
(-3,4)
c)
(3, -4)
d)
(-3,-4)
20.
What is the vertex of y=x2+4x+3?
a)
(2,1)
b)
(-2,1)
c)
(0,0)
d)
(-2,-1)
21.
What is the equation for axis of symmetry? Explain your answer on paper.
a)
y=3
b)
x=3
c)
x=5
d)
x=1
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