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Write a quadratic function with zeros $3$ and $9$ . $\newline$ Write your answer using the variable $x$ and in standard form with a leading coefficient of $1$ . $\newline$ $f(x) =$ ______

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Write a quadratic function from its zeros

Full solution

Q. Write a quadratic function with zeros

3

and

9

.

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

.

\newline

f(x) =

______

Identify Zeros: Zeros are $3$ and $9$ , so factors are $(x - 3)$ and $(x - 9)$ .
Determine Leading Coefficient: Leading coefficient is $1$ , so $f(x) = (x - 3)(x - 9)$ .
Distribute and Expand: Distribute $(x - 3)$ with $(x - 9)$ : $f(x) = x(x - 9) - 3(x - 9)$ .
Multiply $x(x - 9)$ : Multiply $x(x - 9)$ : $x^2 - 9x$ .
Multiply $-3(x - 9)$ : Multiply $-3(x - 9)$ : $-3x + 27$ .
Combine Like Terms: Combine like terms: $f(x) = x^2 - 9x - 3x + 27$ .
Final Function: Final function: $f(x) = x^2 - 12x + 27$ .

More problems from Write a quadratic function from its zeros

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

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Posted 8 months ago

Question

g(x)

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Question

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\newline

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Posted 5 months ago

Question

Write a quadratic function with zeros

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\newline

Write your answer using the variable

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Question

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\newline

\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

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8

f(x) = x^2

\newline

Write your answer in the form

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Posted 4 months ago

Question

x

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Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant