The vertex of this parabola is at (-5, -2). when the x-value is -4, the
y-value is 2. what is the coefficient of the squared expression in the parabola's equation?

a.
1

b.
-1

c.
5

d.
4

Standard form of a parabola is (y-k) =a(x-h)² or y= a(x-h)² +k

The vertex of a parabola is v(h,k).

We have already h & k ( given) ==>v(-5, -2), we still have to calculate "a", the coefficient of the squared expression:
1st info: replace h & k by their respective values: y=a(x+5)² -2
2nd info: when x= -4, y= 2. Replace y & x  in the above equation so that to find a:  2 =a(-4 + 5)² -2==> 2=a(1)² - 2==> a=4 coef. of sqaared expression