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Answer:
f(x) = 2(x + 4)² - 2
Step-by-step explanation:
Equation of quadratic function whose vertex is (h, k),
f(x) = a(x - h)² + k
Equation of the function with vertex (-4, -2) shown in the graph will be,
f(x) = a(x + 4)² - 2
This graph is passing through a point (-6, 6) also,
6 = a(-6 + 4)² - 2
6 + 2 = a(-2)²
a = = 2
Therefore, quadratic function is f(x) = 2(x + 4)² - 2