IXL - Write a quadratic function from its zeros (Algebra 2 practice)

Write a quadratic function with zeros 8 and

–

Write your answer using the variable

and in standard form with a leading coefficient of 1.

(

)

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Learn with an example

question

Write a quadratic function with zeros

–

and

–

Write your answer using the variable

and in standard form with a leading coefficient of 1.

(

)

key idea

The standard form of a polynomial of degree

(

)

is a polynomial and

is a real number such that

(

)

then

is called a zero or a root of

(

)

Factor Theorem

The binomial

(

–

)

is a linear factor of the polynomial

(

)

if and only if

is a zero (or root) of

(

)

Corollary to the Fundamental Theorem of Algebra

(

)

is a polynomial of degree

≥

with complex coefficients, then

(

)

has exactly

complex roots (including any repeated roots).

solution

Use the Factor Theorem to identify the factors. Then, multiply the factors.

Identify the factors.

Each zero corresponds to one linear factor.

Since

–

is a zero,

–

is a factor of

(

)

Since

–

is a zero,

–

is a factor of

(

)

Multiply the factors.

(

)

(

)

(

)

So,

(

)

is a quadratic function with zeros

–

and

–

It is written in standard form with a leading coefficient of 1.

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