Answers Algebra III AQuadratic Functions: Vertex Form

Quadratic Functions: Vertex Form — Unit test Answers

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The step function f(x) is graphed.

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The function f(x) is to be graphed on a coordinate plane.f(x) = At what point should an open circle be drawn?

(–1, 0)

(0, 0)

(0, 1)

(1, 0)

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

The table represents the function f(x).

–29

–10

–3

–1

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

What is the inverse of the function f(x) = x – 12?

h(x) = 48x – 4

h(x) = 48x + 4

h(x) = 4x – 48

h(x) = 4x + 48

Which graph represents the function p(x) = |x – 1|?

Option

Which could be the graph of f(x) = |x - h| + k if h and k are both positive?

Option

Which statement is true of the function f(x) = ? Select three options.The function is always increasing.The function has a domain of all real numbers.The function has a range of {y|– < y < }.The function is a reflection of y = .The function passes through the point (3, –27).

The function is always increasing.

The function has a domain of all real numbers.

The function has a range of {y|– < y < }.

The function is a reflection of y = .

The function passes through the point (3, –27).

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

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.f(x) = Which describes the meaning of f(x)?

A customer earns 1 free night per 10 nights stayed.

A customer starts with 1 free night and then earns another free night after every 10 nights stayed.

A customer earns x – 10 free nights for every 10 nights stayed.

A customer earns 10 free nights after x number of nights stayed.

A function, h(x), is defined as shown.h(x) = Which graph represents h(x)?

Option

What is the simplified form of ?

200

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

(0,8)

(0,–8)

(9,0)

(–9,0)

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

(−4, 18)

(0, -2)

(-8, -2)

(−4, −18)

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).

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 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).