Write a quadratic function with zeros $-9$ and $-7$ . $\newline$ Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$ . $\newline$ $f(x) = \_\_\_\_\_$

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Algebra 2

Write a quadratic function from its zeros

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Q. Write a quadratic function with zeros

-9

and

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Write Factored Form: To find a quadratic function with given zeros, we can start by writing the function in its factored form. The zeros of the function are $-9$ and $-7$ , which means the function will have factors of $(x + 9)$ and $(x + 7)$ . Since the leading coefficient should be $1$ , we do not need to multiply these factors by any other number.
Expand Binomials: Now we will multiply the factors $(x + 9)$ and $(x + 7)$ to find the quadratic function in standard form. We use the distributive property (also known as the FOIL method) to expand the product of these two binomials.
Combine Like Terms: First, we multiply the first terms in each binomial: $x \times x = x^2$ .
Combine Like Terms: First, we multiply the first terms in each binomial: $x \times x = x^2$ .Next, we multiply the outer terms: $x \times 7 = 7x$ .
Combine Like Terms: First, we multiply the first terms in each binomial: $x \times x = x^2$ .Next, we multiply the outer terms: $x \times 7 = 7x$ .Then, we multiply the inner terms: $9 \times x = 9x$ .
Combine Like Terms: First, we multiply the first terms in each binomial: $x \times x = x^2$ .Next, we multiply the outer terms: $x \times 7 = 7x$ .Then, we multiply the inner terms: $9 \times x = 9x$ .Finally, we multiply the last terms in each binomial: $9 \times 7 = 63$ .
Combine Like Terms: First, we multiply the first terms in each binomial: $x \times x = x^2$ .Next, we multiply the outer terms: $x \times 7 = 7x$ .Then, we multiply the inner terms: $9 \times x = 9x$ .Finally, we multiply the last terms in each binomial: $9 \times 7 = 63$ .Now we combine the like terms ( $7x$ and $9x$ ) to get the quadratic function in standard form: $f(x) = x^2 + 16x + 63$ .