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

4/81 = a

Step-by-step explanation:

The vertex form of a parabola is

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

y = a (x- -5)^2 -2

y = a (x+5)^2 -2

Substituting the point into the equation

2 = a( 4+5)^2 -2

2 = a( 9)^2 -2

2 = a (81) -2

Add 2 to each side

4 = 81 a

Divide each side by 81

4/81 = a

207/8 is the right