AnswersFL-1200710-Mathematics for College Algebra ASolving Quadratic Equations: Completing the Square

Modeling with Quadratic Equations Answers

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1
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Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below.What are the solutions to the equation?

Question illustration
A
x = –1, 6
B
x = –6, 1
C
x = –22, 27
D
x = –27, 22
2
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What is the discriminant of the quadratic equation 0 = –x2 + 4x – 2?

A
–4
B
8
C
12
D
24
3

Rhett is solving the quadratic equation 0= x2 – 2x – 3 using the quadratic formula. Which shows the correct substitution of the values a, b, and c into the quadratic formula?Quadratic formula: x =

Question illustration
A
StartFraction 2 plus or minus StartRoot (negative 2) squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option A
B
StartFraction negative 2 plus or minus StartRoot (negative 2) squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option B
C
StartFraction 2 plus or minus StartRoot negative 2 squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option C
D
StartFraction negative 2 plus or minus StartRoot negative 2 squared minus 4(1)(negative 3) EndRoot Over 2(1) EndFraction
Option D
4

Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation x2 + 4x + 8 = 0. Which explanation could Anderson provide?

Question illustration
A
The equation has no real number solutions because the discriminant is 0.
B
The equation has one real number solution because the discriminant is 0.
C
The equation has no real number solutions because the discriminant is less than 0.
D
The equation has two real number solutions because the discriminant is greater than 0.
5

What is the value of the discriminant of the quadratic equation -2x2=-8x+8, and what does its value mean about the number of real number solutions the equation has?

A
The discriminant is equal to 0, which means the equation has no real number solutions.
B
The discriminant is equal to 0, which means the equation has one real number solution.
C
The discriminant is equal to 128, which means the equation has no real number solutions.
D
The discriminant is equal to 128, which means the equation has two real number solutions.
6

What is the discriminant of the quadratic equation 0 = 2x2 + 3x – 5?

A
–37
B
–31
C
43
D
49
7

A quadratic equation of the form 0=ax2+bx+c has a discriminant value of -16. How many real number solutions does the equation have?

A
-1
B
0
C
1
D
2
8

A quadratic equation has a discriminant of 12. Which could be the equation?

A
0 = –x2 + 8x + 2
B
0 = 2x2 + 6x + 3
C
0 = –x2 + 4x + 1
D
0 = 4x2 + 2x + 1
9

What is the discriminant of the quadratic equation 3 – 4x = –6x2?

A
–68
B
–56
C
76
D
88
10

Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x = .

Question illustration
A
Zero, because the discriminant is negative.
B
Zero, because the discriminant is not a perfect square.
C
One, because the negative and the minus cancel each other out.
D
Two, because of the ± symbol.

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