AnswersFL-1200700-Mathematics for College Algebra MISSolving Quadratic Equations: Quadratic Formula

Solving Quadratic Equations: Quadratic Formula — Unit test Answers

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Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

A
(negative 6 minus StartRoot 51 EndRoot comma negative 6 + StartRoot 51 EndRoot)
Option A
B
(negative 6 minus StartRoot 21 EndRoot comma negative 6 + StartRoot 21 EndRoot)
Option B
C
(6 minus StartRoot 51 EndRoot comma 6 + StartRoot 51 EndRoot)
Option C
D
(6 minus StartRoot 21 EndRoot comma 6 + StartRoot 21 EndRoot)
Option D
2
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Which equations are true for x = –2 and x = 2? Select two optionsx2 – 4 = 0x2 = –4 3x2 + 12 = 04x2 = 162(x – 2)2 = 0

A
x2 – 4 = 0
B
x2 = –4
C
3x2 + 12 = 0
D
4x2 = 16
E
2(x – 2)2 = 0
3

What is the first step in solving the quadratic equation -5x2+8=133?

A
taking the square root of both sides of the equation
B
subtracting 8 from both sides of the equation
C
squaring both sides of the equation
D
adding 8 to both sides of the equation
4

A rectangle’s width is 2 meters shorter than its length, l. Its area is 168 square meters. Which equation can be used to find the length of the rectangle?

A
l(l – 2) = 168
B
l(l + 2) = 168
C
2l 2 = 168
D
l 2 = 168
Option D
5

What are the solutions to x2 + 8x + 7 = 0?

A
x = –8 and x = –7
B
x = –7 and x = –1
C
x = 1 and x = 7
D
x = 7 and x = 8
6

Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?Quadratic formula: x =

Question illustration
A
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option A
B
x = StartFraction negative 1 plus or minus StartRoot 1 squared minus 4 (negative 1)(negative 4) EndRoot Over 2(negative 1) EndFraction
Option B
C
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
Option C
D
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 2) EndRoot Over 2(1) EndFraction
Option D
7

Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?

A
(4 minus StartRoot 19 EndRoot comma 4 + StartRoot 19 EndRoot)
Option A
B
(4 minus StartRoot 11 EndRoot comma 4 + StartRoot 11 EndRoot)
Option B
C
(4 minus StartRoot 8 EndRoot comma 4 + StartRoot 8 EndRoot)
Option C
D
(4 minus StartRoot 3 EndRoot comma 4 + StartRoot 3 EndRoot)
Option D
8

Which equation results from taking the square root of both sides of (x – 9)2 = 81?

A
x – 9 = ±9
B
x + 9 = ±9
C
x + 3 = ±9
D
x – 3 = ±9
9

Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x2+3x-8?Quadratic formula: x =

Question illustration
A
1.39
B
2.00
C
2.89
D
3.50
10

The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?

A
x2 + x = 42
B
x2 + 2x = 42
C
x2 + x + 42 = 0
D
x2 + 2x + 42 = 0
11

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below?Quadratic formula: x =

Question illustration
A
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option A
B
x = StartFraction negative 2 plus or minus StartRoot 2 squared minus 4(4)(1) EndRoot Over 2(4) EndFraction
Option B
C
x = StartFraction negative 2 plus or minus StartRoot 2 squared + 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option C
D
x = StartFraction negative 2 plus or minus StartRoot negative 2 squared minus 4(4)(negative 1) EndRoot Over 2(4) EndFraction
Option D
12

Zacharias is using the quadratic formula to solve the equation 0 = –2x2 + 5x – 3. He begins by substituting as shown.Quadratic formula: x = Substitution:

Question illustration
A
The –5 should be 5.
B
The 52 should be –52.
C
The 2 in the numerator should be –2.
D
The 2 in the denominator should be –2.
13

Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?

Question illustration
A
(1, –1)
B
(0, 0) and (0, –1)
C
(0, 0) and (2, 0)
D
no solutions
14

The product of two consecutive integers is 420. Which quadratic equation can be used to find x, the lesser number?

A
x2 + 1 = 420
B
x2 + 2 = 420
C
x2 + x = 420
D
x2 + 2x = 420
15

Which represents the solution(s) of the system of equations, y = x2 – x + 1 and y = x? Determine the solution set by graphing.

A
(1, 1)
B
(0, 1) and (1, 1)
C
(0, 0) and (1, 1)
D
no solutions
16

A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.

A
x2 + (x – 2)2 = 10
B
x2 + 2x2 = 10
C
x2 + (x – 2)2 = 100
D
x2 + 2x2 = 100
18

What are the zeros of the function f(x) = x2 + 5x + 5 written in simplest radical form?Quadratic formula: x =

Question illustration
A
x =
Option A
B
x =
Option B
C
x =
Option C
D
x =
Option D
19

Alessandro wrote the quadratic equation in standard form. What is the value of c in his new equation?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
21

A rectangle’s length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?

A
w2 = 3(243)
B
3w2 = 243
C
4w2 = 243
D
3w2 = 3(243)
22

What are the values of a, b, and c in the quadratic equation 0 = 5x – 4x2 – 2?

A
a = 5, b = 4, c = 2
B
a = 5, b = –4, c = –2
C
a = –4, b = 5, c = –2
D
a = 4, b = –5, c = –2

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