Answers FL-1200710-Mathematics for College Algebra AUnit Test

Unit Test — Unit test Answers

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The function f(x) = –(x – 3)2 + 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

3 square units

6 square units

9 square units

12 square units

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Which equation, when graphed, has x-intercepts at (2, 0) and (4, 0) and a y-intercept of (0, –16)?

f(x) = –(x – 2)(x – 4)

f(x) = –(x + 2)(x + 4)

f(x) = –2(x – 2)(x – 4)

f(x) = –2(x + 2)(x + 4)

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

On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3).

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).

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).

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).

Which quadratic function is the standard form of the equation shown?f(x) = x + 8 + 2x + 5x2

f(x) = 8 + 5x2 + 2x + x

f(x) = x + 2x + 5x2 + 8

f(x) = 8 + 3x + 5x2

f(x) = 5x2 + 3x + 8

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).

g(x) = (x + 5)2 + 2

g(x) = (x + 2)2 + 5

g(x) = (x – 2)2 + 5

g(x) = (x – 5)2 + 2

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

(–2, 0) and (1, 0)

(2, 0) and (1, 0)

(–2, 0) and (-1, 0)

(0, -2) and (0, 1)

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

The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1.

The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4.

The domain is all real numbers, and the range is all real numbers less than or equal to 4.

The domain is all real numbers less than or equal to 4, and the range is all real numbers.

Which point is an x-intercept of the quadratic functionf(x) = (x – 8)(x + 9)?

(0,8)

(0,–8)

(9,0)

(–9,0)

Given the function f(x) = −5x2 − x + 20, find f(3).

−28

−13

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

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).

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).

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).

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).

Consider the function shown on the graph.

f(x) = (x + 3)(x + 7)

f(x) = (x – 3)(x – 7)

f(x) = 3(x – 3)(x – 7)

f(x) = 11(x + 3)(x + 7)

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

all real numbers less than or equal to 4

all real numbers less than or equal to −3

all real numbers greater than or equal to 4

all real numbers greater than or equal to −3

According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold. What is the function that represents this company’s profit f(x) depending on the number of items sold, x?

f(x)=−2(x+105)2+18,050

f(x)=−2(x−105)2+18,050

f(x)=−10(x+105)2+18,050

f(x)=−10(x−105)2+18,050

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 3, negative 2, negative 3, 0, 7.

one-fifth

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).

The domain is all real numbers. The range is {y|y < 16}.

The domain is all real numbers. The range is {y|y ≤ 16}.

The domain is {x|–5 < x < 3}. The range is {y|y < 16}.

The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.

What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?

(−4, 18)

(0, -2)

(-8, -2)

(−4, −18)

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

f(x) = (x − 1)2 + 2

f(x) = (x + 1)2 − 2

f(x) = (x − 2)2 − 1

f(x) = (x + 2)2 − 1

Mary throws a plastic disc to her friend. Her friend catches the disc six seconds after Mary throws it. The table shows the height of the disc at one-second intervals.

A = 5, B = 3

A = 4, B = 0

A = 4, B = 3

A = 5, B = 0

On a coordinate plane, a parabola opens up. It starts in quadrant 1, crosses the x axis where the vertex is in quadrant 4, and crosses the x-axis back into quadrant 1.

f(x) = (x – 8)2 + 6

f(x) = (x + 8)2 + 6

f(x) = (x + 8)2 – 6

f(x) = (x – 8)2 – 6

The graph of which function has a y-intercept of 3?

On a coordinate plane, a parabola opens up. It goes through (negative 3, 3), has a vertex at (negative 1.5, 0.75), and goes through (0, 3).

On a coordinate plane, a parabola opens up. It goes through (1, 4), has a vertex at (3, 0), and goes through (5, 4).

On a coordinate plane, a parabola opens up. It goes through (negative 5, 4), has a vertex at (negative 3, 0), and goes through (negative 1, 4).

On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1, negative 4), and goes through (2, 5).

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