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Solving Quadratic Equations by Quadratic Formula Worksheet - Page 3

Solving Quadratic Equations by Quadratic Formula Worksheet
  • Page 3
 21.  
A tennis player hits a ball when it is 8 feet off the ground. The ball is hit with an upward velocity of 8 feet per second. After the ball is hit, its height h (in feet) is modeled by h = -16t2 + 8t + 8, where t is the time in seconds. How long will it take the ball to reach the ground?
a.
3
b.
4
c.
1
d.
2


Solution:

h = -16t2 + 8t + 8
[Original equation.]

0 = -16t2 + 8t + 8
[Substitute 0 for h, since at ground level the height h = 0.]

t = {-8 ± √[(8)2 - 4(-16)(8)]}/[2(-16)]
[Substitute the values in the quadratic formula: a = -16, b = 8 and c = 8.]

= -8±√(64+512) / -32
[Simplify.]

= -8±√576 / -32
[Simplify inside the radical.]

= -8±24 / -32
[Simplify the radical.]

= -32 / -32 = 1
[Since t represents time, discard negative value.]


Correct answer : (3)
 22.  
Chris drops a ball from a height of 100 feet above the ground. Calculate the time taken by the ball to hit the ground, if its height is given by the equation h = -16t2 + 100, where t is the time in seconds.
a.
3
b.
2.25
c.
2.5
d.
2.75


Solution:

h = -16t2 + 100.
[Original equation.]

0 = -16t2 + 100
[Substituting 0 for h, since at ground level h = 0.]

t = {-0 ± √[(-0)2 - 4(-16)(100)]}/[2(-16)]
[Substitute the values in the quadratic formula: a = -16, b = 0 and c = 100.]

= 0±√(0+6400) / -32
[Simplify.]

= 0±√6400 / -32
[Simplify inside the grouping.]

= 0±80 / -32
[Simplify the radical.]

= -80 / -32 = 2.5
[Since t represents time, rounding it to a positive value.]

So, the ball takes 2.5 sec to reach the ground.


Correct answer : (3)
 23.  
Andy throws a pencil from a building with an initial downward velocity of - 8 feet per second. How long will the pencil take to reach the ground, if the height of the pencil from the ground is modeled by the equation h = - 16t2 - 8t + 48, where t is the time in seconds?
a.
1.5
b.
2
c.
1.75
d.
1.25


Solution:

h = - 16t2 - 8t + 48
[Original equation.]

0 = - 16t2 - 8t + 48
[Substitute values and write in the standard form.]

t = {- (- 8) ± √[(- 8)2 - 4(- 16)(48)]}/2(- 16)
[Substitute the values in the quadratic formula.]

= 8±√(64+3072) / -32
[Simplify.]

= 8±√3136 / -32
[Simplify the radical.]

= 8±56 / -32
[Simplify.]

= -48 / -32 = 1.5
[Evaluating the radical and rounding the solution to a positive value as t represents time.]


Correct answer : (1)
 24.  
What are the values of a, b and c in the equation 4f2 + 3f - 38 = 0, which is in the standard form?
a.
a = -4, b = 3 and c = 38
b.
a = 4, b = 3 and c = -38
c.
a = 4, b = -3 and c = 38
d.
None of the above


Solution:

The standard equation is ax2 + bx + c = 0 when a ≠ 0.

4f2 + 3f - 38 = 0
[Original equation.]

a = 4, b = 3 and c = -38
[Compare the original equation with the standard equation.]


Correct answer : (2)
 25.  
Write the equation 1 3g2 - 3 = - 14 15g in the standard form.
a.
5g2 + 14g - 45 = 0
b.
-5g2 - 14g - 45 = 0
c.
5g2 - 14g - 45 = 0
d.
None of the above


Solution:

13g2 - 3 = - 1415g
[Original equation.]

13g2 - 3 + 1415g = 0
[Add 14 / 15g to each side.]

5g2 - 45 + 14g = 0
[Multiply the equation by LCM, 15.]

5g2 + 14g - 45 = 0
[Rewrite the equation in the standard form.]


Correct answer : (1)

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