The graph of a quadratic function has a vertex at (0, 3) and passes through the poi...
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Problem
The graph of a quadratic function has a vertex at (0, 3) and passes through the points (6, 12) and (-6, 12). Which equation represents the function?
Step-by-step solution
The vertex form of a quadratic function is $f(x) = a(x-h)^2 + k$. Given the vertex $(h, k) = (0, 3)$, the function is $f(x) = ax^2 + 3$. Using the point $(6, 12)$, we get $12 = a(6)^2 + 3$, which simplifies to $9 = 36a$, so $a = 1/4$. Thus, the equation is $f(x) = \frac{1}{4}x^2 + 3$.
Answer
f(x) = 1/4 x^2 + 3