Answers FL-1200710-Mathematics for College Algebra AUnit Test

Unit Test — Unit test Answers

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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.

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The curve produced by the water coming from a fountain is sketched on the graph.

f(x) = (x – 2)2 + 3

f(x) = –(x – 2)2 + 3

f(x) = (x + 2)2 + 3

f(x) = –(x + 2)2 + 3

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

right 5, down 23

left 5, down 23

right 5, up 27

left 5, up 27

Which function has a vertex on the y-axis?

f(x) = (x – 2)2

f(x) = x(x + 2)

f(x) = (x – 2)(x + 2)

f(x) = (x + 1)(x – 2)

On a coordinate plane, a parabola opens up. It goes through (negative 3.25, 5), has a vertex of (1.75, negative 2.75), and goes through (6.25, 5). Solid circles appear on the parabola at (negative 3, 4), (0, negative 2), (1.75, negative 2.75), (3, negative 2), (6, 4).

–2

–0.5

1.5

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

All-Star Trinkets estimates its monthly profits using a quadratic function. The table shows the total profit as a function of the number of trinkets produced.

f(x) = –4(x – 50)(x – 250)

f(x) = (x – 50)(x – 250)

f(x) = 28(x + 50)(x + 250)

f(x) = (x + 50)(x + 250)

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.

Which is the graph of the function f(x) = x2 + 2x + 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 (1, 2), and goes through (2, 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).

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).

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 6x + 6?

left 3 units, down 3 units

right 3 units, down 3 units

left 6 units, down 1 unit

right 6 units, down 1 unit

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

all real numbers less than or equal to 7

all real numbers greater than or equal to 7

all real numbers less than or equal to −3

all real numbers greater than or equal to −3

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

Robin’s graph is a reflection of Giselle’s graph over the x-axis.

Robin’s graph is a reflection of Giselle’s graph over the y-axis.

Robin’s graph is a translation of Giselle’s graph 1 unit down.

Robin’s graph is a translation of Giselle’s graph 1 unit left.

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?

The graph of f(x) = x2 is widened.

The graph of f(x) = x2 is shifted right 4 units.

The graph of f(x) = x2 is shifted down 36 units.

The graph of f(x) = x2 is reflected over the x-axis.

The function f(x) = –x2 – 4x + 5 is shown on the graph.

The domain of the function is all real numbers less than or equal to −2.

The domain of the function is all real numbers less than or equal to 9.

The range of the function is all real numbers less than or equal to −2.

The range of the function is all real numbers less than or equal to 9.

Consider the quadratic function f(x) = x2 – 8x – 4. What is the value of the leading coefficient?

–8

–4

The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form.

f(x) = (x + 2)2 + 3

f(x) = (x2 + 2x)2 + 3

f(x) = (x + 1)2 + 2

f(x) = (x + 3)2 + 2x

The graph of the function f(x) = (x + 2)(x − 4) is shown.

all real values of x where x < −2

all real values of x where −2 < x < 4

all real values of x where 1 < x < 4

all real values of x where x < 0

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.

The value of f(–10) = 82

The graph of the function is a parabola.

The graph of the function opens down.

The graph contains the point (20, –8).

The graph contains the point (0, 0).

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

The domain is {x| x ≥ 3}.

The range is {y| y ≥ –1}.

The function decreases over the interval (–∞, 3).

The axis of symmetry is x = –1.

The vertex is (3, –1).

Jan'ai was asked to determine the minimum for a function with zeros located at –1 and 5, which also has a y-intercept of (0, –25). Her work is shown.Which best describes the first error in Jan'ai's work?

She incorrectly determined the factors for the beginning function.

She incorrectly determined the a value.

She incorrectly transformed the equation to standard form.

She incorrectly determined the x-coordinate of the vertex.

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