The function f is defined by f(x) = x^2 + bx + c, where b and... | SAT Nonlinear functions Question, Answer Explained

Math · Advanced MathMedium

The function $f$ is defined by $f(x) = x^2 + bx + c$ , where $b$ and $c$ are constants. The graph of $y = f(x)$ in the $xy$ -plane has its vertex at $(3, -4)$ . What is the value of $c$ ?

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Answer: 5

The leading coefficient is $1$ and the vertex is $(3, -4)$ , so $f(x) = (x - 3)^2 - 4 = x^2 - 6x + 9 - 4 = x^2 - 6x + 5$ . So $c = 5$ .

Answering $-4$ treats the $y$ -coordinate of the vertex as the constant term, but $c$ is $f(0)$ , which is $9 - 4 = 5$ .

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