Quadratic Formula Worksheet

**Page 3**

21.

A stone is dropped from a height of 9 feet above the ground. The height of the stone is modeled by the equation $h$ = - 16$t$^{2} + 9, where $t$ is the time in seconds. Find the time taken for the stone to hit the ground.

a. | 0.75 | ||

b. | 1 | ||

c. | 1.25 | ||

d. | 0.5 |

[Original equation.]

0 = - 16

[Replace

[Substitute the values in the quadratic formula:

=

[Simplify.]

[Simplify inside the radical.]

=

[Simplify the radical.]

[Since

Correct answer : (1)

22.

Tim runs a textile company that manufactures T-shirts. The profit made by the company is modeled by the function $p$ = $s$^{2} + 9$s$ - 1620, where $s$ is the number of T-shirts sold. Find the least number of T-shirts to be sold so that Tim does not end up in a loss.

a. | 40 | ||

b. | 36 | ||

c. | 42 | ||

d. | 38 |

[Original equation.]

0 =

[Replace

[Substitute the values in the quadratic formula:

=

[Simplify.]

=

[Simplify inside the radical.]

=

[Simplify the radical.]

[Consider only the positive value of

Correct answer : (2)

23.

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 $h$ = - 16$t$^{2} + 8$t$ + 8, where $t$ is the time in seconds. How long will it take the ball to reach the ground?

a. | 4 | ||

b. | 3 | ||

c. | 2 | ||

d. | 1 |

[Original equation.]

0 = - 16

[Replace

[Substitute the values in the quadratic formula:

=

[Simplify.]

=

[Simplify inside the radical.]

=

[Simplify the radical.]

=

[Since

Correct answer : (4)

24.

Chris drops a ball from a height of 64 feet above the ground. Calculate the time taken by the ball to hit the ground, if its height is given by the equation $h$ = - 16$t$^{2} + 64, where $t$ is the time in seconds.

a. | 1.75 | ||

b. | 2.5 | ||

c. | 2.25 | ||

d. | 2 |

[Original equation.]

0 = - 16

[Substituting 0 for

[Substitute the values in the quadratic formula:

=

[Simplify.]

=

[Simplify inside the grouping.]

=

[Simplify the radical.]

=

[Since

So, the ball takes 2 sec to reach the ground.

Correct answer : (4)

25.

Sunny 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 $h$ = - 16$t$^{2} - 8$t$ + 48, where $t$ is the time in seconds?

a. | 2 | ||

b. | 1.5 | ||

c. | 1.75 | ||

d. | 1.25 |

[Original equation.]

0 = - 16

[Substitute values and write in the standard form.]

[Substitute the values in the quadratic formula.]

=

[Simplify.]

=

[Simplify the radical.]

=

[Simplify.]

=

[Evaluating the radical and taking the positive value since

Correct answer : (2)

26.

What are the values of $a$, $b$ and $c$ in the equation 2$f$ ^{2} - 8$f$ + 22 = 0, which is in the standard form?

a. | $a$ = 2, $b$ = - 8 and $c$ = 22 | ||

b. | $a$ = -2, $b$ = 8 and $c$ = - 22 | ||

c. | $a$ = 2, $b$ = 22 and $c$ = 0 | ||

d. | $a$ = - 2, $b$ = - 8 and $c$ = 22 |

2

[Original equation.]

[Compare the original equation with the standard equation.]

Correct answer : (1)

27.

Write the equation which is used to model the height of an object that is thrown down with an initial velocity of - 8 feet per second from a height of 18 feet.

a. | $h$ = - 16$t$ ^{2} + 8$t$ + 18 | ||

b. | $h$ = - 16$t$ ^{2} + 18 | ||

c. | $h$ = - 16$t$ ^{2} - 8$t$ + 18 | ||

d. | $h$ = - 16$t$ ^{2} - 8$t$ - 18 |

[Model for an object which is thrown from an initial height '

[Substitute

Therefore, the equation of an object that is thrown down with an initial velocity of - 8 feet per second from a height of 18 feet is

Correct answer : (3)