IXL - Write a quadratic function in standard form from its x-intercepts and another point (Algebra 2 practice)

Write the equation of the parabola that passes through the points

(

)

(

–

)

and

(

–

)

Write your answer in standard 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 standard form,

where

and

are integers, decimals, or simplified fractions.

key idea

A parabola with

-intercepts

and

has an equation of the form

(

–

)

(

–

)

This can be expanded into the standard form of a parabola,

solution

The parabola passes through the points

(

–

)

(

–

)

and

(

)

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

–

and 3. Substitute these values for

and

in the equation

(

–

)

(

–

)

(

–

)

(

–

)

(

–

(

–

)

(

–

)

(

)

(

–

)

To find

plug in the

and

-coordinates

of the other point,

(

–

)

(

)

(

–

)

(

–

)

(

–

)

(

)

(

–

)

–

Substitute the value

–

into the equation of the parabola.

(

)

(

–

)

–

(

)

(

–

)

Finally, expand the equation to put it into standard form.

–

(

)

(

–

)

Multiply the binomials

–

(

–

)

Multiply the binomials

Combine like terms

–

(

–

)

Combine like terms

Distribute

–

Distribute

Looking for more? Try these:

Lesson: Quadratic equations

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Not feeling ready yet? These can help:

N.12Write a quadratic function in factored form from its x-intercepts and another point

W.8Multiply two binomials

C.7Solve one-step linear equations

Lesson: Quadratic equations

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