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.