Write a quadartic function in standard form whose maximum value is 6 and occurs when x=-2.

y = x² + 4x + 10

Step-by-step 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

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step-by-step explanation:

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