Quadratic Formula Worksheet

**Page 1**

1.

Solve the equation $\frac{1}{4}$$k$^{2} - 4$k$ + 12 = 0 by using the quadratic formula.

a. | $k$ = - 4, 12 | ||

b. | $k$ = - 4, - 12 | ||

c. | $k$ = 4, 12 | ||

d. | $k$ = 4, - 12 |

[Original equation.]

[Multiply the equation by 4.]

[Substitute

[Simplify inside the radical.]

[Write ± as two separate equations.]

[Simplify.]

Correct answer : (3)

2.

Solve the system:

$x$^{2} + $y$^{2} = 17

$y$ - $x$ = 4

[Original system of equations.]

[Rearrange eq (2).]

[Use (

[Substitute

2

[Simplify.]

[Use the quadratic formula

=

[Simplify.]

= - 2 ±

[Simplify.]

[Substitute

[Simplify.]

[Substitute

[Simplify.]

So, the solutions are (- 2 +

Correct answer : (0)

3.

Which of the following are the solutions of the quadratic equation $\mathrm{ax}$^{2} + $\mathrm{bx}$ + $c$ = 0, when $a$ ≠ 0 and $b$^{2} - 4$\mathrm{ac}$ ≥ 0?

a. | $x$ = $\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$ | ||

b. | $x$ = $\frac{b\pm \sqrt{{b}^{2}-4ac}}{2}$ | ||

c. | $x$ = - $\frac{b}{a}$ and $x$ = $\frac{c}{a}$ | ||

d. | $x$ = - $\frac{a}{b}$ and $x$ = $\frac{c}{b}$ |

Correct answer : (1)

4.

Write the equation - $d$^{2} + 3 = 5$d$ - 5$d$^{2} in the standard form.

a. | 4$d$ ^{2} + 5$d$ - 3 = 0 | ||

b. | 4$d$ ^{2} - 5$d$ + 3 = 0 | ||

c. | 4$d$ ^{2} - 5$d$ - 3 = 0 | ||

d. | 4$d$ ^{2} + 5$d$ + 3 = 0 |

[Original equation.]

4

[Add 5

4

[Subtract 5

4

[Rewrite the equation in the standard form.]

Correct answer : (2)

5.

What are the values of $a$, $b$ and $c$ in the quadratic formula used to solve the equation 5$e$^{2} - 4 + $e$ = - $e$^{2} + 5$e$?

a. | $a$ = 6, $b$ = - 4 and $c$ = 4 | ||

b. | $a$ = 6, $b$ = 4 and $c$ = - 4 | ||

c. | $a$ = 6, $b$ = - 4 and $c$ = - 4 | ||

d. | $a$ = - 6, $b$ = - 4 and $c$ = - 4 |

[Original equation.]

6

[Add

6

[Subtract 5

6

[Rewrite the equation in the standard form.]

In the quadratic formula,

So,

Correct answer : (3)

6.

What are the values of $a$, $b$ and $c$ in the equation 4$f$ ^{2} - 2$f$ + 33 = 0, which is in the standard form?

a. | $a$ = 4, $b$ = - 2 and $c$ = 33 | ||

b. | $a$ = 4, $b$ = 2 and $c$ = 33 | ||

c. | $a$ = 4, $b$ = 2 and $c$ = - 33 | ||

d. | $a$ = - 4, $b$ = - 2 and $c$ = - 33 |

4

[Original equation.]

[Compare the original equation with the standard equation.]

Correct answer : (1)

7.

Write the equation $\frac{1}{3}$$g$^{2} - 2 = - $\frac{11}{12}$$g$, in the standard form.

a. | $\frac{1}{3}$$g$ ^{2} - $\frac{11}{12}$$g$ + 2 = 0 | ||

b. | $\frac{1}{3}$$g$ ^{2} + $\frac{11}{12}$$g$ - 2 = 0 | ||

c. | $\frac{1}{3}$$g$ ^{2} - $\frac{11}{12}$$g$ - 2 = 0 | ||

d. | $\frac{1}{3}$$g$ ^{2} + $\frac{11}{12}$$g$ + 2 = 0 |

[Original equation.]

[Add

[Rewrite the equation in the standard form.]

Correct answer : (2)

8.

Find the value of $b$^{2} - 4$a$$c$, for the equation -8$x$^{2} - 20$x$ - 12 = 0.

a. | 784 | ||

b. | - 784 | ||

c. | 404 | ||

d. | 16 |

[Original equation.]

8

[Rewrite the equation in the standard form.]

[Compare the equation with standard equation

[Replace

= 16

[Simplify.]

Correct answer : (4)

9.

Find the solutions of the quadratic equation $p$^{2} + 7$p$ + 12 = 0.

a. | - 3, - 4 | ||

b. | 3, 4 | ||

c. | 7, 12 | ||

d. | - 19 |

[Original equation.]

[Substitute

[Simplify.]

[Simplify.]

[Simplify.]

Correct answer : (1)

10.

Jeff throws a pen from the top of a 124 feet tall building with an initial downward velocity of - 30 feet per second. How long will the pen take to reach the ground?

a. | 2 | ||

b. | 30 | ||

c. | 124 | ||

d. | - 3.785 |

[Original equation.]

0 = - 16

[Height = 0, when the pen is on the ground.]

Compare the original equation with the standard form to get the values of

[Substitute the values in the quadratic formula.]

[Evaluate power and multiply.]

=

[Simplify the radical.]

= - 3.875, 2

[Simplify.]

The ball reaches the ground after 2 seconds.

[Consider positive value as

Correct answer : (1)

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