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 $h$ = -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. | 3 | ||

b. | 4 | ||

c. | 1 | ||

d. | 2 |

[Original equation.]

0 = -16

[Substitute 0 for

[Substitute the values in the quadratic formula:

=

[Simplify.]

=

[Simplify inside the radical.]

=

[Simplify the radical.]

=

[Since

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 $h$ = -16$t$^{2} + 100, where $t$ is the time in seconds.

a. | 3 | ||

b. | 2.25 | ||

c. | 2.5 | ||

d. | 2.75 |

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

a. | 1.5 | ||

b. | 2 | ||

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 rounding the solution to a positive value as

Correct answer : (1)

24.

What are the values of $a$, $b$ and $c$ in the equation 4$f$^{2} + 3$f$ - 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 |

4

[Original equation.]

[Compare the original equation with the standard equation.]

Correct answer : (2)

25.

Write the equation $\frac{1}{3}$$g$^{2} - 3 = - $\frac{14}{15}$$g$ in the standard form.

a. | 5$g$ ^{2} + 14$g$ - 45 = 0 | ||

b. | -5$g$ ^{2} - 14$g$ - 45 = 0 | ||

c. | 5$g$ ^{2} - 14$g$ - 45 = 0 | ||

d. | None of the above |

[Original equation.]

[Add

5

[Multiply the equation by LCM, 15.]

5

[Rewrite the equation in the standard form.]

Correct answer : (1)