IXL - Write equations of parabolas in vertex form from graphs (Algebra 2 practice)

The graph shows a parabola and its focus. 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

A parabola is the set of points in a plane that are the same distance from a fixed line and a fixed point that is not on the line. The fixed line lies outside the parabola and is called the

directrix.

The fixed point lies inside the parabola and is called the

focus.

The vertex form of a parabola that opens up or down is

(

–

)

The vertex is

(

)

the parabola opens up. If

the parabola opens down.

The distance from the vertex to the focus and the directrix is

It is called the focal length or focal distance.

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 down, 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 down,

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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Work it out

Not feeling ready yet? These can help:

DD.2Find the vertex of a parabola

DD.3Find the focus or directrix of a parabola

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