SAT
Nonlinear functions
Multiple choice

Find a quadratic from its intercepts

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The graph of the quadratic function $g$ has $x$ -intercepts at $(-3,0)$ and $(8,0)$ and passes through the point $(2,-60)$ . Which of the following equations defines $g$ ?

Select one answer.

g(x)=2(x+3)(x-8)

g(x)=(x+3)(x-8)

g(x)=2(x-3)(x+8)

g(x)=2(x-3)(x-8)

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Answer: A ( $g(x)=2(x+3)(x-8)$ )

The $x$ -intercepts show that $x=-3$ and $x=8$ are zeros of $g$ , so $g(x)=a(x+3)(x-8)$ for some constant $a$ . Since the graph passes through $(2,-60)$ , substituting $x=2$ and $g(2)=-60$ gives $-60=a(2+3)(2-8)=-30a$ . Therefore, $a=2$ , and $g(x)=2(x+3)(x-8)$ .

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