The equation of the quadratic function graphed is: y = -1/4 (x + 2)² + 3
How to write the equation
Quadratic equation in standard vertex form si
y = a(x - h)² + k
where a = 1/4p
The vertex
v (h, k) = (-2,-3)
h = -2
k = 3
The graph passed through (-4, 2) we use it to solve for a
2 = a(-4 - (-2))² + 3
2 - 3 = a(-4+ 2)²
-1 = a(-2)²
-1 = a * 4
a = -1/4
Plugging in the values we have the equation
y = -1/4 (x + 2)² + 3