college algebra

/in /by

college algebra

Question 1 (5 points)

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = 2(x – 3)2 + 1

Question 1 options:

Question 2 (5 points)

Solve the following polynomial inequality.

3x2 + 10x – 8 ≤ 0

Question 2 options:

Question 3 (5 points)

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

g(x) = x + 3/x(x + 4)

Question 3 options:

Question 4 (5 points)

If f is a polynomial function of degree n, then the graph of f has at most __________ turning points.

Question 4 options:

Question 5 (5 points)

8 times a number subtracted from the squared of that number can be expressed as:

Question 5 options:



P(x) = x + 7x.

P ( x ) = x + 7 x .



P(x) = x2 − 8x.

P ( x ) = x 2 – 8 x .



P(x) = x − x.

P ( x ) = x – x .



P(x) = x2+ 10x.

P ( x ) = x 2 + 10 x .

Question 6 (5 points)

Solve the following polynomial inequality.

9x2 – 6x + 1 < 0

Question 6 options:

Question 7 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = -2x4 + 4x3

Question 7 options:

Question 8 (5 points)

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3).

Question 8 options:

f(x) = 2(x – 5)2 + 3

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

Question 9 (5 points)

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = -2(x + 1)2 + 5

Question 9 options:

Question 10 (5 points)

Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function.

f(x) = x/x + 4

Question 10 options:

Question 11 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x3 + 2x2 – x – 2

Question 11 options:

Question 12 (5 points)

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2 – 7x + 5)/x – 4 is:

Question 12 options:

y = 3x2 + 7.

Question 13 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x2(x – 1)3(x + 2)

Question 13 options:

Question 14 (5 points)

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum.

Minimum = 0 at x = 11

Question 14 options:



f(x) = 6(x − 9)

f ( x ) = 6 ( x – 9 )



f(x) = 3(x − 11)2

f ( x ) = 3 ( x – 11 )



f(x) = 4(x + 10)

f ( x ) = 4 ( x + 10 )



f(x) = 3(x2 − 15)2

f ( x ) = 3 ( x 2 – 15 )

Question 15 (5 points)

The graph of f(x) = -x2 __________ to the left and __________ to the right.

Question 15 options:

Question 16 (5 points)

Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x4 – 9x2

Question 16 options:

Question 17 (5 points)

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.

f(x) = x3 – x – 1; between 1 and 2

Question 17 options:

Question 18 (5 points)

40 times a number added to the negative square of that number can be expressed as:

Question 18 options:



A(x) = x2 + 20x.

A ( x ) = x 2 + 20 x .



A(x) = −x + 30x.

A ( x ) = – x + 30 x .



A(x) = −x2 − 60x.

A ( x ) = – x 2 – 60 x .



A(x) = −x2 + 40x.

A ( x ) = – x 2 + 40 x .

Question 19 (5 points)

Find the domain of the following rational function.

f(x) = x + 7/x2 + 49

Question 19 options:

Question 20 (5 points)

The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as:

Question 20 options: