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

Solving Quadratic Equations: Quadratic Formula — Unit test Answers

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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.
2
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What is the solution to 2x2+8x=x2-16?

A
x=-4
B
x=-2
C
x=2
D
x=4
3

What are the x-intercepts of the function f(x) = –x2 – x + 2?

A
(–2, 0) and (1, 0)
B
(2, 0) and (1, 0)
C
(–2, 0) and (-1, 0)
D
(0, -2) and (0, 1)
4

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
5

Which function has an axis of symmetry of x = −2?

A
f(x) = (x − 1)2 + 2
B
f(x) = (x + 1)2 − 2
C
f(x) = (x − 2)2 − 1
D
f(x) = (x + 2)2 − 1
6

Which function is a quadratic function?

A
a(x) = –2x3 + 2x – 6
B
b(x) = 5x3 + 8x2 + 3
C
c(x) = –8x2 + 3x – 5
D
d(x) = 6x4 + 2x – 3
7

Which is the graph of f(x) = x2 – 2x + 3?

A
On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (negative 1, 2), and goes through (0, 3).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (2, negative 1), and goes through (4, 3).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 4, 3), has a vertex at (negative 2, negative 1), and goes through (0, 3).
Option D
8

The function f(x) = −(x + 5)(x + 1) is shown.

Question illustration
A
all real numbers less than or equal to 4
B
all real numbers less than or equal to −3
C
all real numbers greater than or equal to 4
D
all real numbers greater than or equal to −3
9

Which graph represents the function f(x) = –x2 + 5?

A
On a coordinate plane, a parabola opens down. It goes through (negative 3, negative 4), has a vertex at (0, 5), and goes through (3, negative 4).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 2, 9), has a vertex at (0, 5), and goes through (2, 9).
Option B
C
On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 9), has a vertex at (negative 5, 0), and goes through (negative 2, negative 9).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 8, 9), has a vertex at (negative 5, 0), and goes through (negative 2, 10).
Option D
10

The graph of the function f(x) = –(x + 3)(x – 1) is shown below.

Question illustration
A
The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1.
B
The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4.
C
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
D
The domain is all real numbers less than or equal to 4, and the range is all real numbers.
11

Which function is a quadratic function?

A
y – 3x2 = 3(x2 + 5) + 1
B
y2 – 7x = 2(x2 + 6) + 7
C
y – 2x2 = 6(x3 + 5) – 4
D
y – 5x = 4(x + 5) + 9
12

What are the solutions of the quadratic equation (x + 3)2 = 49?

A
x = –2 and x = –16
B
x = 2 and x =
Option B
C
x = 4 and x = –10
D
x = 40 and x = –58
13

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
14

Which are the roots of the quadratic function f(q) = q2 – 125? Select two options.

Question illustration
A
q = 5
Option A
B
q = -5
Option B
C
q = 3
Option C
D
q = -3
Option D
E
q = 25
Option E
15

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
16

A rectangle has an area of 40 square units. The length is 6 units greater than the width.

A
8 by 5
B
10 by 4
C
11 by 9
D
13 by 7
17

Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = after substituting the values of a, b, and c into the formula. Which is Ramiya’s quadratic equation?Quadratic formula: x =

Question illustration
A
0 = x2 + 3x + 2
B
0 = x2 – 3x + 2
C
0 = 2x2 + 3x + 1
D
0 = 2x2 – 3x + 1
18

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
19

On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).

Question illustration
A
The domain is all real numbers. The range is {y|y < 16}.
B
The domain is all real numbers. The range is {y|y ≤ 16}.
C
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
D
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.
20

On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (3, 6), has a vertex at (5, 2), and goes through (7, 6).

Question illustration
A
g(x) = (x + 5)2 + 2
B
g(x) = (x + 2)2 + 5
C
g(x) = (x – 2)2 + 5
D
g(x) = (x – 5)2 + 2

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