IXL - Write equations of parabolas in vertex form (Precalculus practice)

The graph shows a parabola and its directrix. Write the equation of the parabola in vertex form.

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question

The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.

key idea

solution

To write the parabola in vertex form, find the vertex and focus. Then, solve for the dilation factor

Finally, plug in the vertex coordinates and the dilation factor.

Find the vertex and focus.

Look at the graph to find the vertex and focus.

The vertex is

(

)

and the focus is

(

–

)

Also, notice that the parabola opens left, so it has the form

(

–

)

with

Solve for the dilation factor

To find the dilation factor

first find

the distance between the vertex and the focus. Since the vertex

(

)

and the focus

(

–

)

have the same

-coordinate,

0, the distance between them is the absolute value of the difference in their

-coordinates:

–

Now use

to solve for

Since the parabola opens left,

So,

–

Plug in the vertex coordinates and the dilation factor

The equation of the parabola in vertex form is:

(

–

)

Plug in

–

and

–

(

–

)

Plug in

–

and

–

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Teacher tools

Work it out

Not feeling ready yet? These can help:

U.1Find properties of parabolas

DD.5Write equations of parabolas in vertex form from graphs

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