# college algebra 24

## 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:
 (3, 1) (7, 2) (6, 5) (2, 1)

## Question 2 (5 points)

Solve the following polynomial inequality.

3x2 + 10x – 8 ≤ 0

Question 2 options:
 [6, 1/3] [-4, 2/3] [-9, 4/5] [8, 2/7]

## 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:
 Vertical asymptotes: x = 4, x = 0; holes at 3x Vertical asymptotes: x = -8, x = 0; holes at x + 4 Vertical asymptotes: x = -4, x = 0; no holes Vertical asymptotes: x = 5, x = 0; holes at x – 3

## 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:
 n – 3 n – f n – 1 n + f

## 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:
 (-∞, -3) (-1, ∞) [2, 4) Ø

## 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:
 x = 1, x = 0; f(x) touches the x-axis at 1 and 0 x = -1, x = 3; f(x) crosses the x-axis at -1 and 3 x = 0, x = 2; f(x) crosses the x-axis at 0 and 2 x = 4, x = -3; f(x) crosses the x-axis at 4 and -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) = 2x2, but with the given point as the vertex (5, 3).

Question 8 options:
 f(x) = (2x – 4) + 4 f(x) = 2(2x + 8) + 3 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:
 (-1, 5) (2, 10) (1, 10) (-3, 7)

## 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:
 Vertical asymptote: x = -4; no holes Vertical asymptote: x = -4; holes at 3x Vertical asymptote: x = -4; holes at 2x Vertical asymptote: x = -4; holes at 4x

## 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:
 x = 2, x = 2, x = -1; f(x) touches the x-axis at each. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each. x = -3, x = -4, x = 1; f(x) touches the x-axis at each. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each.

## 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 = 3x + 5. y = 6x + 7. y = 2x – 5. 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:
 x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2 and 3; f(x) touches the x-axis at -1 x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6 and 3; f(x) touches the x-axis at 2. x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7 and 2; f(x) touches the x-axis at 0. x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2 and 1; f(x) touches the x-axis at 0.

## 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:
 falls; rises rises; rises falls; falls rises; rises

## 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:
 x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.

## 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:
 f(1) = -1; f(2) = 5 f(1) = -3; f(2) = 7 f(1) = -1; f(2) = 3 f(1) = 2; f(2) = 7

## 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:
 All real numbers < 69 All real numbers > 210 All real numbers ≤ 77 All real numbers

## 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:
 80 + x. 20 – x. 40 + 4x. 40 – x.

##### Do you need a similar assignment done for you from scratch? We have qualified writers to help you. We assure you an A+ quality paper that is free from plagiarism. Order now for an Amazing Discount! Use Discount Code "Newclient" for a 15% Discount!NB: We do not resell papers. Upon ordering, we do an original paper exclusively for you. 