The graph of a quadratic function has a vertex at the origin and passes through the...
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Problem
The graph of a quadratic function has a vertex at the origin and passes through the points (2, -16) and (-2, -16). Which equation represents the function?
Step-by-step solution
A quadratic function with a vertex at the origin has the form $f(x) = ax^2$. Substituting the point $(2, -16)$ gives $-16 = a(2^2)$, so $-16 = 4a$, which means $a = -4$. Thus, the function is $f(x) = -4x^2$.
Answer
f(x) = -4x^2