Answer:
y = x² + 4x + 10
Explanation:
Given the maximum value = 6 when x = - 2, then
vertex = (- 2, 6)
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier, thus
y = a(x - (- 2))² + 6 ← let a = 1
y = (x + 2)² + 6 ← equation in vertex form
Expand factor and simplify
y = x² + 4x + 4 + 6, that is
y = x² + 4x + 10 ← in standard form