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# find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given x-intercepts. (There are many correct answers.) (4, 0), (8, 0)

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The $x$-intercepts are $(4, 0)$ and $(8, 0)$ This means that the solutions of the function are $x = 4$ and $x = 8$. Write these as factors of the function. Let $a$ be the opening of the parabola, whether upward or downward.

\begin{aligned} f(x) = a(x - 4)(x - 8) \end{aligned}

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