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f(x) = - 2 (x + 2)² + 6

Step-by-step explanation:

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

Here (h, k) = (- 2, 6), thus

y = a(x - (- 2))² + 6, that is

y = a(x + 2)² + 6

To find a substitute the point (0, - 2) into the equation

- 2 = a(0 + 2)² + 6 ( subtract 6 from both sides )

- 8 = 4a ( divide both sides by 4 )

- 2 = a

f(x) = - 2(x + 2)² + 6 ← in vertex form

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step-by-step explanation: