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Write a quadratic function with zeros $4$ and $-9$ . $\newline$ Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$ . $\newline$ $g(x) =$ $\_\_\_\_\_$

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Write a quadratic function from its zeros

Full solution

Q. Write a quadratic function with zeros

4

and

-9

.

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

.

\newline

g(x) =

\_\_\_\_\_

Identify Zeros: Zeros are $4$ and $-9$ , so factors are $(x - 4)$ and $(x + 9)$ .
Determine $g(x)$ Function: $g(x) = 1 \times (x - 4) \times (x + 9)$ .
Distribute Terms: Distribute $(x + 9)$ with $x$ and $-4$ . $g(x) = x(x + 9) - 4(x + 9)$ .
Multiply $x$ and $(x + 9)$ : Multiply $x$ and $(x + 9)$ . $\newline$ $x(x + 9) = x^2 + 9x$ .
Multiply $-4$ and $(x + 9)$ : Multiply $-4$ and $(x + 9)$ . $\newline$ $-4(x + 9) = -4x - 36$ .
Combine Like Terms: Combine like terms. $\newline$ $g(x) = x^2 + 9x - 4x - 36$ .
Final Result: $g(x) = x^2 + 5x - 36$ .

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