IXL - Write a quadratic function from three points (Algebra 2 practice)

Write an equation of the parabola that passes through the points

(

–

)

(

–

)

and

(

)

Write your answer in the form

where

and

are integers.

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Learn with an example

question

Write an equation of the parabola that passes through the points

(

–

)

(

)

and

(

–

)

Write your answer in the form

where

and

are integers.

solution

A parabola passes through the points

(

–

)

(

)

and

(

–

)

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

Notice that one of the points,

(

–

)

tells you that the

-intercept

is equal to

–

So,

–

You can also see this by plugging the

and

-coordinates

(

–

)

into the equation.

–

(

)

(

)

–

So, plug

–

into the equation of the parabola.

(

–

)

–

Now, plug the

and

-coordinates

of the other two points into the equation. You can start with the point

(

–

)

–

(

–

)

(

–

)

–

The other point,

(

)

will give you another equation. Together, the two equations form a system of equations with the unknowns

and

(

–

)

↦

–

(

)

↦

Use this system of equations to solve for

and

You can use elimination to solve the system. To solve for

multiply both sides of the second equation by 2 so the equations have opposite

terms. Then, add the equations to eliminate

–

(

)

(

)

To solve for

plug

into either equation. This shows how to use the first equation:

–

(

)

–

So,

and

–

Use these values to write the equation of the parabola.

(

)

(

)

(

–

)

–

Looking for more? Try this:

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Work it out

Not feeling ready yet? These can help:

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

E.13Solve a system of equations in three variables using elimination

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