The graph of y = -x^2-5x + 36 intersects the x-axis at two points, A and B. The length of line segment AB is

A. 9

B. 13

C. 5

D. 36

If f(x)=x^2+5x+3k and f(k)=-16, f(2) equals

A. -4

B. -16

C. -2

D. 2

The minimum distance between the parabolas y = -5x^2 - 8 and y = 7x^2 + 6 is

A. 14

B. 12

C. 8

D. 6

A quadratic function of the form f(x) = ax^2 + bx + c has roots x = \frac{-3 \pm \sqrt{31}}{2}. The graph of the function passes through the point (1, -3). What is the equation of the function?

A. \displaystyle f(x) = 2x^2 -6x + 11

B. \displaystyle f(x) = 2x^2 +6x - 11

C. \displaystyle f(x) = 3x^2 - 2\sqrt{5}x - 4

D. \displaystyle f(x) = 2x^2 + 2\sqrt{5}x -3

The sum, S, and product, P, of the roots of the function f(x) = -3x^2 + 24x + 477 are

A. S = 24, P = 477

B. S = 24, P = 1437

C. S = 8, P = -159

D. S = -8, P = 159

If x^y = 4, then the value of x^{3y}-x^{2y} is

A. 48

B. 64

C. 4

D. 12

If M = 5^x + 5^{-x} and N = 5^x =5^{-x}, then the value fo M^2 -N^2 is

A. 2(5^{2x})

B. 2(5^{-2x})

C. 4

D. 0

In the given diagram, XY = X2 = 15 and YZ = 18. The value of \sin Z is

A. \displaystyle \frac{3}{5}

B. \displaystyle \frac{4}{5}

C. \displaystyle \frac{4}{9}

D. \displaystyle \frac{4}{3}

Explain why the minimum value of (x - a)^2 + (x - b)^2 occurs when x = \frac{a + b}{2}. What is the minimum value.