# 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 2 (5 points)

Solve the following polynomial inequality.

3x^{2} + 10x – 8 ≤ 0

## 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 4 (5 points)

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

## Question 5 (5 points)

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

## Question 6 (5 points)

Solve the following polynomial inequality.

9x^{2} – 6x + 1 < 0

## 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) = -2x^{4} + 4x^{3}

## Question 8 (5 points)

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

## Question 12 (5 points)

Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x^{2} – 7x + 5)/x – 4 is:

## 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) = x^{2}(x – 1)^{3}(x + 2)

## Question 14 (5 points)

Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x^{2} or g(x) = -3x^{2}, but with the given maximum or minimum.

Minimum = 0 at x = 11

## Question 15 (5 points)

The graph of f(x) = -x^{2} __________ to the left and __________ to the right.

## Question 16 (5 points)

f(x) = x^{4} – 9x^{2}

## Question 17 (5 points)

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

f(x) = x^{3} – x – 1; between 1 and 2

## Question 18 (5 points)

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

## Question 19 (5 points)

Find the domain of the following rational function.

f(x) = x + 7/x^{2} + 49

## 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: