Question

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?

Answer 1

in vertex the parabola is

y = a(x -b)^2 + c

vertex is at
(-5,-2) s0

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

x = -4 when y = 2 so

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

a = 4

therefor
4 is the coefficient of x^2 in the parabola's equation