The vertex of this parabola is at (4, -3). when the x-value is 5, the
y-value is -6. what is the coefficient of the squared expression in the parabola's equation?

a.3 b.2 c.-3. d.-2

Formula for parabola is y = a(x - h)^2 + k where vertex is (h,k)

Given:  vertex is (4, -3)  plus this into the equation h = 4 and k = -3
 
y = a(x - 4)^2 + -3

Given: x-value is 5 the y-value is -6  plug these numbers in to solve for a.

-6 = a (5 - 4) ^2 +-3
-6 = a (1)^2 + -3     add 3 to both sides
-6 + 3 = a (1) +-3 + 3
-3 = a
the coefficient "a" is -3

Enjoy!  :-)