The equation of the quadratic function graphed is: y = (x + 1)² + 2
How to write the equation
Quadratic equation in standard vertex form is
y = a(x - h)² + k
The vertex
v (h, k) = (-1, 2)
h = -1
k = 2
The graph passed through (0, 3) we use it to solve for a
x = 0, y = 3
y = a(x - h)² + k
3 = a(0 - (-1))² + 2
3 - 2 = a(0 + 1)²
1 = a
a = 1
Plugging in the values we have the equation
y = (x + 1)² + 2