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I need help with my college algebra school work with 20 questions multiply questions.  I've attached the questions.

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).

A. f(x) = (2x - 4) + 4

B. f(x) = 2(2x + 8) + 3

C. f(x) = 2(x - 5)2 + 3

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

.Write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as y and z

A. x = kz; y = x/k

B. x = kyz; y = x/kz

C. x = kzy; y = x/z

D. x = ky/z; y = x/zk

The graph of f(x) = -x3 __________ to the left and __________ to the right.

A. rises; falls

B. falls; falls

C. falls; rises

D. falls; falls

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)

A. x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2

and 3; f(x) touches the x-axis at -1

B. x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6

and 3; f(x) touches the x-axis at 2.

C. x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7

and 2; f(x) touches the x-axis at 0.

D. x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2

and 1; f(x) touches the x-axis at 0.

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) = -3x2, but with the given maximum or minimum.

Maximum = 4 at x = -2

A. f(x) = 4(x + 6)2 - 4

B. f(x) = -5(x + 8)2 + 1

C. f(x) = 3(x + 7)2 - 7

D. f(x) = -3(x + 2)2 + 4

Find the domain of the following rational function.

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

A. All real numbers &lt; 69

B. All real numbers &gt; 210

C. All real numbers ? 77

D. All real numbers

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

A. y = 3x + 5.

B. y = 6x + 7.

C. y = 2x - 5.

D. y = 3x2 + 7.

Solve the following polynomial inequality.

9x2 - 6x + 1 &lt; 0

A. (-?, -3)

B. (-1, ?)

C. [2, 4)

D. Ø

The difference between two numbers is 8. If one number is represented by x, the other number can be

expressed as:

A. x - 5.

B. x + 4.

C. x - 8.

D. x - x.

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

A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3

and 3; f(x) touches the x-axis at 0.

B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2

and 3; f(x) crosses the x-axis at 0.

C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3

and 5; f(x) touches the x-axis at 0.

D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2

and -4; f(x) touches the x-axis at 0.

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

A. falls; rises

B. rises; rises

C. falls; falls

D. rises; rises

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

A.

A(x) = x2 + 20x.

B. A(x) = -x + 30x.

C.

A(x) = -x2 - 60x.

D.

A(x) = -x2 + 40x.

Find the domain of the following rational function.

g(x) = 3x2/((x - 5)(x + 4))

A. {x? x ? 3, x ? 4}

B. {x? x ? 4, x ? -4}

C. {x? x ? 5, x ? -4}

D. {x? x ? -3, x ? 4}

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

A. P(x) = x + 7x.

B.

P(x) = x2 - 8x.

C. P(x) = x - x.

D.

P(x) = x2+ 10x.

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

A. x = 2, x = 2, x = -1; f(x) touches the x-axis at

each.

B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at

each.

C. x = -3, x = -4, x = 1; f(x) touches the x-axis at

each.

D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at

each.

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

f(x) = 2(x - 3)2 + 1

A. (3, 1)

B. (7, 2)

C. (6, 5)

D. (2, 1)

Determine the degree and the leading coefficient of the polynomial function f(x) = -2x 3 (x - 1)(x + 5).

A. 5; -2

B. 7; -4

C. 2; -5

D. 1; -9

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

A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0

B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3

C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2

D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

Solve the following polynomial inequality.

3x2 + 10x - 8 ? 0

A. [6, 1/3]

B. [-4, 2/3]

C. [-9, 4/5]

D. [8, 2/7]

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

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

A. (-1, 5)

B. (2, 10)

C. (1, 10)

D. (-3, 7)

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This question was answered on: Feb 21, 2020

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