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

Solving Quadratic Equations: Quadratic Formula — Unit test Answers

15 verified answers
1
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What are the solutions to the quadratic equation 4(x + 2)2 = 36

A
x = −11 and x = 7
B
x = −7 and x = 11
C
x = −5 and x = 1
D
x = −1 and x = 5
2
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three

Question illustration
T
The vertex is the maximum value.
T
The axis of symmetry is x = .
Option T
T
The domain is all real numbers.
T
The range is all real numbers.
T
The function is decreasing from (−∞, 6.75).
3

Which statements are true about the graph of the function h(x) = –5x2 + 60x – 200? Select three options.The axis of symmetry is the line x = –6.The graph of h(x) will not intersect the graph of the parent function, f(x) = x2.The vertex of the graph is at (6, –20).The parabola has a maximum.The value of k, when the equation is written in vertex form, is –200.

A
The axis of symmetry is the line x = –6.
B
The graph of h(x) will not intersect the graph of the parent function, f(x) = x2.
C
The vertex of the graph is at (6, –20).
D
The parabola has a maximum.
E
The value of k, when the equation is written in vertex form, is –200.
4

What is the axis of symmetry of h(x) = 6x2 − 60x + 147?

A
x = −5
B
x = −3
C
x = 3
D
x = 5
5

The steps in writing f(x)=18x+3x2 in vertex form are shown, but a value is missing in the last step.Write the function in standard form. Factor a out of the first two terms. f(x)=3(x2+6x)Form a perfect square trinomial. f(x)=3(x2+6x+9)−3(9) Write the trinomial as a binomial squared. f(x)=3(x+___)2−27

Question illustration
A
3
B
6
C
9
D
18
6

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 9x2 – 36x?

A
The graph of f(x) = x2 is widened.
B
The graph of f(x) = x2 is shifted right 4 units.
C
The graph of f(x) = x2 is shifted down 36 units.
D
The graph of f(x) = x2 is reflected over the x-axis.
7

What is the range of the function f(x) = −(x + 3)2 + 7?

A
all real numbers less than or equal to 7
B
all real numbers greater than or equal to 7
C
all real numbers less than or equal to −3
D
all real numbers greater than or equal to −3
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

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
10

Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Select three options.

A
The domain is {x| x ≥ 3}.
B
The range is {y| y ≥ –1}.
C
The function decreases over the interval (–∞, 3).
D
The axis of symmetry is x = –1.
E
The vertex is (3, –1).
11

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
12

Giselle graphs the function f(x) = x2. Robin graphs the function g(x) = –x2. How does Robin’s graph relate to Giselle’s?

R
Robin’s graph is a reflection of Giselle’s graph over the x-axis.
R
Robin’s graph is a reflection of Giselle’s graph over the y-axis.
R
Robin’s graph is a translation of Giselle’s graph 1 unit down.
R
Robin’s graph is a translation of Giselle’s graph 1 unit left.
13

Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options.5(x2 + 4x + 4) = –7 + 20x + 2 = 5(x2 + 4x) = 75(x2 + 4x + 4) = 7 + 205(x2 + 4x) = –7

Question illustration
A
5(x2 + 4x + 4) = –7 + 20
B
x + 2 =
C
5(x2 + 4x) = 7
D
5(x2 + 4x + 4) = 7 + 20
E
5(x2 + 4x) = –7
14

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

The function f(x) = –3x2 + 36x – 119 written in vertex form is f(x) = –3(x – 6)2 – 11. Which statements are true about the graph of f(x)? Select three options.

A
The axis of symmetry is the line x = 6.
B
The vertex of the graph is at (–6, –11).
C
The parabola has a minimum.
D
The parabola opens down.
E
The value of h, when the equation is written in vertex form, is positive.

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