IXL - Write a quadratic function in factored form from its x-intercepts and another point (Algebra 1 practice)

Write the equation of the parabola that passes through the points

(

–

)

(

)

and

(

)

Write your answer in the form

(

–

)

(

–

)

where

and

are integers, decimals, or simplified fractions.

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Learn with an example

question

Write the equation of the parabola that passes through the points

(

)

(

)

and

(

–

)

Write your answer in the form

(

–

)

(

–

)

where

and

are integers, decimals, or simplified fractions.

key idea

A parabola with

-intercepts

and

has an equation of the form

(

–

)

(

–

)

solution

The parabola passes through the points

(

)

(

)

and

(

–

)

You want to write the equation of the parabola in the form

(

–

)

(

–

)

Notice that the

-coordinates

of two of the points,

(

)

and

(

–

)

are 0, so those points lie on the

-axis.

That means the parabola has

-intercepts

at 4 and

–

Substitute these values for

and

in the equation.

(

–

)

(

–

)

(

–

)

(

–

(

–

)

(

–

)

(

)

To find

plug in the

and

-coordinates

of the other point,

(

)

(

–

)

(

)

(

–

)

(

)

(

–

)

(

)

–

Use the value

–

to finish writing the equation of the parabola.

(

–

)

(

)

–

(

–

)

(

)

Looking for more? Try these:

Lesson: Quadratic equations

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C.7Solve one-step linear equations

Lesson: Quadratic equations

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