Relating a Quadratic Function and Its Zeros

8.11.1 Relating a Quadratic Function and Its Zeros

8.11.1 • Relating a Quadratic Function and Its Zeros

Warm Up

Write the quadratic function $f (x) = x^{2} - 9 x + 20$ in factored form.

Compare your answer:

$f (x) = (x - 4) (x - 5)$

What are the solutions of the quadratic equation $(x - 4) (x - 5) = 0$ ?

Compare your answer:

$x = 4$ and $x = 5$

Graph the quadratic function $f (x) = x^{2} - 9 x + 20$ .

Use the Desmos graphing tool or technology outside the course.

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What are the $x$ -intercepts of the graph?

Compare your answer:

$(4, 0)$ , $(5, 0)$ or 4 and 5

Marcus states that the zeros of the function of $f (x) = x^{2} - 9 x + 20$ are 4 and 5. Do you agree? Be prepared to show your reasoning.

Compare your answer:

Yes, 4 and 5 are the input values that result in an output of 0. When the function $f (x) = x^{2} - 9 x + 20$ is graphed, it crosses the $x$ -axis at $x = 4$ and $x = 5$ .