Write a quadratic function, in vertex form, whose graph has a vertex at (-4, -2) an...
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Problem
Write a quadratic function, in vertex form, whose graph has a vertex at (-4, -2) and passes through the points (-2, 6) and (-6, 6).
Step-by-step solution
The vertex form of a quadratic function is $f(x) = a(x-h)^2 + k$. Given the vertex $(h, k) = (-4, -2)$, we have $f(x) = a(x+4)^2 - 2$. Using the point $(-2, 6)$, we substitute to find $a$: $6 = a(-2+4)^2 - 2 \implies 8 = 4a \implies a = 2$. Thus, the function is $f(x) = 2(x+4)^2 - 2$.
Answer
f(x)=2(x+4)^2-2