AnswersCR27 ALG 1-1200310-S2-Degele-VOL7006PIntroduction to Quadratic Functions

Lesson 8.1: Introduction to Quadratic Functions Answers

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On a coordinate plane, a parabola opens up. It goes through (negative 7.5, 4), has a vertex of (negative 3, negative 9), and goes through (1.5 4). Solid circles appear on the parabola at (negative 7, 1.75), (negative 6, negative 3), (negative 3, negative 9), (0, negative 3), (1, 1.75).

Question illustration
A
–9
B
–3
C
0
D
9
2
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Which function increases at the fastest rate between x = 0 and x = 8?

A
A 2-column table with 5 rows titled Linear Function with the equation f of x = 2 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 6, 10, 14, 18.
Option A
B
A 2-column table with 5 rows titled Exponential Function with the equation f of x = 2 Superscript x Baseline + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 3, 6, 18, 66, 258.
Option B
C
A 2-column table with 5 rows titled Quadratic Function with the equation f of x = 2 x squared + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 10, 34, 74, 130.
Option C
D
A 2-column table with 5 rows titled Linear Function with the equation f of x = 3 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 8, 14, 20, 26.
Option D
3

Which graph represents a quadratic function with a vertex at (0, 0)?

A
On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 1), and goes through (5, 6).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 6, 6), has a vertex of (0, negative 1), and goes through (6, 6).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 2.5, 6), has a vertex of (3, 0), and goes through (7.5, 4).
Option D
4

Which graph shows a negative rate of change for the interval 0 to 2 on the x-axis?

A
On a coordinate plane, a parabola opens up. It goes through (negative 6, 3), has a vertex of (negative 1.5 negative 3.75), and goes through (3.2, 4).
Option A
B
On a coordinate plane, a parabola opens up. It goes through (negative 5.5, 4), has a vertex of (negative 1, negative 3.2), and goes through (3.5, 4).
Option B
C
On a coordinate plane, a parabola opens up. It goes through (negative 1, 4), has a vertex of (2.5, 0.25), and goes through (5.8, 4).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 3.4, 4), has a vertex of (1.5, negative 3.75), and goes through (6, 3).
Option D
5

Which represents a quadratic function?

A
f(x) = 2x3 + 2x2 – 4
B
f(x) = –7x2 – x + 2
C
f(x) = –3x + 2
D
f(x) = 0x2 + 3x – 3
6

When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown?2 + 7c – 4c2 – 3c + 4

A
–4c2 + 4c + 6
B
–7c2 + 10c + 6
C
–4c2 + 4c + 8
D
–7c2 + 7c + 6
7

What possible changes can Martha make to correct her homework assignment? Select two options.

A
The first term, 5x3, can be eliminated.
B
The exponent on the first term, 5x3, can be changed to a 2 and then combined with the second term, 2x2.
C
The exponent on the second term, 2x2, can be changed to a 3 and then combined with the first term, 5x3.
D
The constant, –3, can be changed to a variable.
E
The 7x can be eliminated.
8

Consider the quadratic function f(x)=8x2−7x+6. What is the constant of the function?

A
−7
B
6
C
7
D
8
9

A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 21, 10, 5, 6, 13.

Question illustration
A
f(x) = 3x2 + 2x – 5
B
f(x) = 3x2 – 2x + 5
C
f(x) = 2x2 + 3x – 5
D
f(x) = 2x2 – 2x + 5
10

When the polynomial is written in standard form, what are the values of the leading coefficient and the constant?5x + 2 – 3x2

A
The leading coefficient is 5, and the constant is 2.
B
The leading coefficient is 2, and the constant is 5.
C
The leading coefficient is –3, and the constant is 2.
D
The leading coefficient is 2, and the constant is –3.

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