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: