#If 1 and -2 are two zeros of the polynomial x3-4x2-7x+10

[excellentideasineducation]

If the square of the difference of the zeros of the quadratic polynomial...

[tutorsof]

Math Assignment-6

Question - 1

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. 

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

Question - 2

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0.

A. horizontal asymptotes 

B. polynomial 

C. vertical asymptotes 

D. slant asymptotes

Question - 3

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.

Question - 4

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

f(x) = 2x4 - 4x2 + 1; between -1 and 0

A. f(-1) = -0; f(0) = 2 

B. f(-1) = -1; f(0) = 1 

C. f(-1) = -2; f(0) = 0 

D. f(-1) = -5; f(0) = -3

Question - 5

"Y varies directly as the nth power of x" can be modeled by the equation:

A. y = kxn. 

B. y = kx/n. 

C. y = kx*n. 

D. y = knx.

Question - 6

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

A. y = 3x + 5. 

B. y = 6x + 7. 

C. y = 2x - 5. 

D. y = 3x2 + 7.

Question - 7

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

Question - 8

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

A. Vertical asymptote: x = -4; no holes 

B. Vertical asymptote: x = -4; holes at 3x 

C. Vertical asymptote: x = -4; holes at 2x 

D. Vertical asymptote: x = -4; holes at 4x

Question - 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) = 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

Question - 10

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

A. n - 3 

B. n - f 

C. n - 1 

D. n + f

Question - 11

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.

Question - 12

9x2 - 6x + 1 < 0

A. (-∞, -3) 

B. (-1, ∞) 

C. [2, 4) 

D. Ø

Question - 13

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]

Question - 14

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

A. f(x) = 6(x - 9) 

B. f(x) = 3(x - 11)2 

C. f(x) = 4(x + 10) 

D. f(x) = 3(x2 - 15)2

Question - 15

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).

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

Question - 16

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)

Question - 17

Determine the degree and the leading coefficient of the polynomial function f(x) = -2x3 (x - 1)(x + 5).

A. 5; -2 

B. 7; -4 

C. 2; -5 

D. 1; -9

Question - 18

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

A. f(1) = -1; f(2) = 5 

B. f(1) = -3; f(2) = 7 

C. f(1) = -1; f(2) = 3 

D. f(1) = 2; f(2) = 7

Question - 19

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)

A. Vertical asymptotes: x = 4, x = 0; holes at 3x 

B. Vertical asymptotes: x = -8, x = 0; holes at x + 4 

C. Vertical asymptotes: x = -4, x = 0; no holes 

D. Vertical asymptotes: x = 5, x = 0; holes at x – 3

Question - 20

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