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Linear and Quadratic Functions Worksheet

Linear and Quadratic Functions Worksheet
  • Page 1
 1.  
A small stone is projected directly upward from the ground with an initial velocity of 32 ft/s. Write an equation to find the time t for the stone to reach a height of 64 ft.
a.
16t2 + 32t + 64 = 0
b.
32t2 + 16t - 64 = 0
c.
16t2 + 64t+ 32 = 0
d.
16t2 - 32t + 64 = 0


Solution:

The velocity of projection is u = 32 ft/s

The height reached by the vertically projected stone in t sec is h = ut - 16t2
[Use the laws of motion for a vertically projected body.]

64 = 32t - 16t2
[Replace h = 64 ft and u = 32 ft/s to find the time for the stone to reach the height 64 ft.]

16t2 - 32t + 64 = 0


Correct answer : (4)
 2.  
In a zoo, there are some apes. 4 apes are on the trees and the number of remaining apes is equal to the square of one-fifth of their total number. Choose the total number of apes from the following.
a.
20
b.
16
c.
4
d.
10


Solution:

Total number of apes = 4 + (1 / 5 of total number of apes)2
[Aanalyze the situation.]

n = 4 + n²25
[Let the total number of apes = n.]

n2 - 25n + 100 = 0
[Multiply each term with 25 and rearrange.]

(n - 20)(n - 5) = 0
[Factor.]

n - 20 = 0 or n - 5 = 0

n =20 or n = 5
[Solve for n.]

The number of apes in the forest is either 20 or 5.


Correct answer : (1)
 3.  
There are three consecutive positive integers. If the product of the first two integers is 2 more than 9 times the third integer, then find the integers.
a.
2, 3, 4
b.
8, 9, 10
c.
10, 11, 12
d.
6, 7, 8


Solution:

The consecutive integers are x, x + 1, x + 2
[Let the first positive integer be x.]

x(x + 1) = 2 + 9(x + 2)
[Analyze the situation.]

x2 + x = 2 + 9x + 18
[Use the Distributive property.]

x2 - 8x - 20 = 0
[Group the terms and simplify.]

(x - 10)(x + 2) = 0
[Factor.]

x = 10 or x = - 2
[Solve for x.]

x = 10
[x is positive.]

The consecutive positive integers are 10, 11, 12.


Correct answer : (3)
 4.  
Find the sides of a right triangle which are consecutive integers.
a.
5, 6, 7
b.
cannot be determined
c.
3, 4, 5
d.
2, 3, 4


Solution:

The sides of the right triangle are x, x + 1, and x + 2
[Let the short leg of the right triangle = x, and analyze the situation.]

x2 + (x + 1)2 = (x + 2)2
[Use the Pythagorean theorem.]

x2 + x2 + 2x + 1 = x2 + 4x + 4
[Use (a + b)2 = a2 + 2ab + b2, and expand.]

x2 - 2x - 3 = 0
[Group the terms and simplify.]

(x - 3)(x + 1) = 0
[Factor.]

x = 3 or x = - 1
[Solve for x.]

x = 3
[The length of the side of a triangle cannot be negative.]

The sides of the right triangle are 3 units, 4 units, and 5 units.


Correct answer : (3)
 5.  
In a zoo, there are some apes. 6 apes are on the trees and the number of remaining apes is equal to the square of one-seventh of their total number. Choose the total number of apes from the following.
a.
42
b.
41
c.
49
d.
43


Solution:

Total number of apes = 6 + (1 / 7 of total number of apes)2
[Aanalyze the situation.]

n = 6 + n²49
[Let the total number of apes = n.]

n2 - 49n + 294 = 0
[Multiply each term with 49 and rearrange.]

(n - 42)(n - 7) = 0
[Factor.]

n - 42 = 0 or n - 7 = 0

n =42 or n = 7
[Solve for n.]

The number of apes in the forest is either 42 or 7.


Correct answer : (1)
 6.  
Find the rate of change of the linear function y = 7x + 10.
a.
10
b.
- 10
c.
7
d.
- 7


Solution:

The rate of change of the linear function y = 7x + 10 is 7.
[The rate of change of the linear function y = mx + b is m.]


Correct answer : (3)
 7.  
Find the leading coefficient of the given function (p) = 29.
a.
29
b.
1
c.
2


Solution:

The leading coefficient of a polynomial function is the coefficient of highest degree variable in it.

Here, the polynomial function is (p) = 29.

(p) = 29 · p0
[Rewrite (p) using p0 = 1.]

So, the leading coefficient of (p) is 29.


Correct answer : (2)
 8.  
What is the lower bound of the correlation coefficient r?
a.
1
b.
- 2
c.
- 1


Solution:

The correlation coefficient r [- 1, 1] and hence its lower bound is -1.


Correct answer : (4)
 9.  
What is the upper bound the correlation coefficient r?
a.
1
b.
2
c.
-1


Solution:

The correlation coefficient r [- 1, 1] and hence its upper bound is 1.


Correct answer : (1)
 10.  
Write the degree of the polynomial function (v) = 8v11 + 46.
a.
11
b.
8
c.
13


Solution:

The degree of the polynomial function f (x) = an xn + an-1 xn-1 + ... + a2 x2 + a1 x + a0 is n.

So, the degree of the polynomial function (v) = 8v11 + 46 is 11.


Correct answer : (1)

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