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Write a quadratic function with zeros $-9$ and $-3$ . $\newline$ 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

-9

and

-3

.

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

.

\newline

g(x) =

______

Identify Zeros: Identify the linear factors from the zeros $-9$ and $-3$ , which are $(x + 9)$ and $(x + 3)$ .
Multiply Factors: Multiply the linear factors to get the quadratic function: $g(x) = (x + 9)(x + 3)$ .
Distribute Terms: Distribute the terms: $g(x) = x(x + 3) + 9(x + 3)$ .
Multiply x Terms: Multiply $x$ with $(x + 3)$ : $x(x) + x(3) = x^2 + 3x$ .
Multiply $9$ Terms: Multiply $9$ with $(x + 3)$ : $9(x) + 9(3) = 9x + 27$ .
Combine Like Terms: Combine like terms: $g(x) = x^2 + 3x + 9x + 27$ .
Add $x$ Terms: Add the $x$ terms: $g(x) = x^2 + 12x + 27$ .

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