The vertex of this parabola is at (-4, -1). when the y-value is 0, the x-value is 2. what is the coefficient of the squared term in the parabola's equation?

a.3 b.-6 c.-3 d.6

Equation for parabola is
y = a ( x - h ) ^2 + k    where (h,k) is the vertex of the parabola. 

Given:  vertex (-4, -1)  h = -4; k = -1

y = a (x - (-4))^2 + (-1)
y = a ( x + 4)^2 - 1  plug in the values given for x and y.  y-value is 0 and x-value is 2

0 = a (2 + 4)^2 -1
0 = a (6)^2 -1   square 6
0 = a 36 - 1    add 1 to both sides to isolate the a
1 = 36 a         divide both sides by 36 to isolate the a
1/36 = a         the coefficient. 

i think you might have typed a number incorrectly if those are your answer choices.  Maybe the step by step process can still help you with your correct numbers.  :-) 

Looks pretty good to me!