AnswersFL-1200710-Mathematics for College Algebra ASolving Quadratic Equations: Quadratic Formula

Solving Quadratic Equations: Quadratic Formula — Unit test Answers

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1
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A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation?

A
–5
B
0
C
1
D
6
2
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The function g(x) is defined as g(x) = 6x2 + 23x – 4. When does g(x) = 0?

Question illustration
x
x = –6 or x =
Option x
x
x = –4 or x =
Option x
x
x = or x = 6
Option x
x
x = or x = 4
Option x
3

What are the solutions to m2 – 9 = 0?

m
m = –9 and m = 0
m
m = –3 and m = 3
m
m = –3
m
m = 9
4

Which is the graph of a quadratic equation that has a negative discriminant?

A
On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (negative 4, negative 4), has a vertex at (negative 2, 0), and goes through (0, negative 4).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 4, 4), has a vertex at (negative 2, 0), and goes through (0, 4).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 4, 8), has a vertex at (negative 2, 4), and goes through (0, 8).
Option D
5

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = −2x2 − 3x + 8, and what does it mean about the number of real solutions the equation has?

A
The discriminant is −55, so the equation has 2 real solutions.
B
The discriminant is −55, so the equation has no real solutions.
C
The discriminant is 73, so the equation has 2 real solutions.
D
The discriminant is 73, so the equation has no real solutions.
6

Which is a solution to the equation?(x − 3)(x − 5) = 35

A
x = −8
B
x = −5
C
x = 2
D
x = 10
7

A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation?

A
0 = 2x2 – 4x + 1
B
0 = 2x2 – 5x + 3
C
0 = –2x2 – 4x – 2
D
0 = –2x2 – 3x – 1
8

Which equation has an a-value of –2, a b-value of 1, and a c-value of 3?

A
0 = –2x2 + x + 3
B
0 = 2x2 + x + 3
C
0 = –2x2 + 3
D
0 = 2x2 – x + 3
9

Mischa wrote the quadratic equation 0=-x2+4x-7 in standard form. If a = -1, what is the value of c in her equation?

A
c=-7
B
c=-1
C
c=4
D
c=7
10

What is a solution to (x + 6)(x + 2) = 60?

A
x = −6
B
x = −4
C
x = 4
D
x = 12
11

Which function has real zeros at x = −10 and x = −6?

f
f(x) = x2 + 16x + 60
f
f(x) = x2 − 16x + 60
f
f(x) = x2 + 4x + 60
f
f(x) = x2 − 4x + 60
12

Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing?

f
f(x) = x2 + 36x + 12
f
f(x) = x2 – 36x – 12
f
f(x) = –x2 + 12x + 36
f
f(x) = –x2 – 12x – 36
13

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

A
(m – 5)(m + 5) = 99
B
(m – 10)(m + 10) = 99
C
m2 – 25 = –99
D
m2 – 100 = –99
14

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle?

A
7
B
15
C
20
D
28
15

Between which two ordered pairs does the graph of f(x) = x2 + x – 9 cross the negative x-axis?Quadratic formula: x =

Question illustration
A
(–6, 0) and (–5, 0)
B
(–4, 0) and (–3, 0)
C
(–3, 0) and (–2, 0)
D
(–2, 0) and (–1, 0)

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