AnswersCommon Core Algebra I 2014 - MA3109 B-CRSolving Quadratic Equations: Completing the Square

Solving Quadratic Equations: Completing the Square — Unit test Answers

24 verified answers7 views
21
Free Preview

The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?

Question illustration
A
mc022-2.jpg
Option A
B
mc022-3.jpg
Option B
C
mc022-4.jpg
Option C
D
mc022-5.jpg
Option D
22
Free Preview

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

A
x = −5
B
x = −3
C
x = 3
D
x = 5
23

Which function is a quadratic function?

A
f(x) = 2x2
B
g(x) = 5x3
C
k(x) = –x
D
b(x) = –9x4
24

Why is the product of a rational number and an irrational number irrational?

A
because the product is always a non-terminating, non-repeating decimal
B
because the product is always a fraction
C
because the product is always a negative number
D
because the product is always a repeating or a terminating decimal
25

Fiona is completing the square to solve the polynomial equation.x2 – 4x + 1 = 0

A
isolating the constant 1
B
adding 4 to both sides of the equation
C
isolating the second term, –4x
D
adding 1 to both sides of the equation
26

The length of a rectangular field is represented by the expression . The width of the field is represented by the expression . How much greater is the length of the field than the width?

Question illustration
A
mc026-3.jpg
Option A
B
mc026-4.jpg
Option B
C
mc026-5.jpg
Option C
D
mc026-6.jpg
Option D
27

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

A
{–7, 1}
B
(negative 3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)
Option B
C
(3 minus StartRoot 10 EndRoot comma negative 3 + StartRoot 10 EndRoot)
Option C
D
{1, 7}
28

Holly finds that (11m – 13n + 6mn) – (10m – 7n + 3mn) = m – 20n + 9mn. What error did Holly make?

A
She only used the additive inverse of 10m when combining like terms.
B
She added the polynomials instead of subtracting.
C
She only used the additive inverses of –7n and 3mn when combining like terms.
D
She did not combine all like terms.
29

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

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.
30

Which of the following expresses as a fraction in simplest form?

Question illustration
A
mc003-2.jpg
Option A
B
mc003-3.jpg
Option B
C
mc003-4.jpg
Option C
D
mc003-5.jpg
Option D
31

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
32

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
33

Which expression shows the sum of the polynomials with like terms grouped together?

Question illustration
A
mc004-2.jpg
Option A
B
mc004-3.jpg
Option B
C
mc004-4.jpg
Option C
D
mc004-5.jpg
Option D
34

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)
35

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.
36

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
37

What is the vertex of the graph of y + 2x + 3 = –(x + 2)2 + 1?

A
(–3, –33)
B
(–3, 3)
C
(3, –24)
D
(3, 21)
38

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.
39

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
40

Which graph represents an inverse variation?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

Did you find these answers helpful?

More from this Course

Quiz
15 verified answers

Unit Test

Quiz
15 verified answers

Unit Test

Assignment
23 verified answers

Solving Quadratic Equations: Completing the Square