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Write a quadratic function with zeros $2$ 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

2

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 $2$ and $9$ , so factors are $(x - 2)$ and $(x - 9)$ .
Write Function: $f(x) = 1 \times (x - 2) \times (x - 9)$ .
Distribute Terms: Distribute $(x - 9)$ with $x$ and $-2$ . $f(x) = x(x - 9) - 2(x - 9)$ .
Multiply $x$ : Multiply $x$ and $(x - 9)$ . $\newline$ $x(x - 9) = x^2 - 9x$ .
Multiply $-2$ : Multiply $-2$ and $(x - 9)$ . $\newline$ $-2(x - 9) = -2x + 18$ .
Combine Like Terms: Combine like terms. $f(x) = x^2 - 9x - 2x + 18$ .
Final Function: $f(x) = x^2 - 11x + 18$ .

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

`m` = ____ or `m` = _____

Posted 8 months ago

Question

g(x)

g(x)

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5

f(x)=x^2

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Write your answer in the form

a(x–h)^2+k

a

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Question

What is the range of this quadratic function?

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y = x^2 - 4x + 4

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\left\{y \mid y \geq 2\right\}

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\left\{y \mid y \geq 0\right\}

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\text{all real numbers}

Posted 5 months ago

Question

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\newline

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\newline

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\newline

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\newline

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Posted 5 months ago

Question

Write a quadratic function with zeros

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-7

\newline

Write your answer using the variable

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and in standard form with a leading coefficient of

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\newline

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

Posted 5 months ago

Question

Find the equation of the axis of symmetry for the parabola

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Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

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g(x) =

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Posted 4 months ago

Question

x

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Write your answer in simplified, rationalized form.

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x =

\newline

Posted 5 months ago

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