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Write a quadratic function with zeros $5$ and $-5$ . $\newline$ 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

5

and

-5

.

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

.

\newline

g(x) =

______

Zeroes Identification: Zeroes of the function: $5$ and $-5$ . $\newline$ Identify the linear factors using the zeros. $\newline$ If $5$ is a zero, then $(x - 5)$ is a factor. $\newline$ If $-5$ is a zero, then $(x + 5)$ is a factor.
Linear Factors: Leading coefficient: $1$ . $\newline$ Linear factors: $(x - 5)$ and $(x + 5)$ . $\newline$ The quadratic function in factored form is $f(x) = (x - 5)(x + 5)$ .
Factored Form: Expand the factored form to get the standard form. $f(x) = (x - 5)(x + 5) = x^2 + 5x - 5x - 25$ .
Expand and Simplify: Combine like terms. $\newline$ $f(x) = x^2 - 25$ .

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)

g(x)

is the translation

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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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\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}

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\newline

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\newline

Write your answer using the variable

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\underline{\hspace{3cm}}

Posted 4 months ago

Question

g(x)

g(x)

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f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

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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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