The function f is defined by f(x) = a(x - 3)^2 + 7, where a... | SAT Nonlinear functions Question, Answer Explained

Math · Advanced MathHard

The function $f$ is defined by $f(x) = a(x - 3)^2 + 7$ , where $a$ is a constant. The graph of $y = f(x)$ in the $xy$ -plane passes through the point $(5, -1)$ . What is the value of $f(0)$ ?

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Answer: -11

Substitute the point: $-1 = a(5 - 3)^2 + 7 = 4a + 7$ , so $4a = -8$ and $a = -2$ . Then $f(0) = -2(0 - 3)^2 + 7 = -2(9) + 7 = -11$ .

Treating $(0 - 3)^2$ as $-9$ gives $f(0) = 25$ , but squaring $-3$ gives $9$ .

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