IXL - Write equations of parabolas in vertex form from graphs (Geometry 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 directrix. 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 directrix. Then, solve for the dilation factor

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

Find the vertex and directrix.

Look at the graph to find the vertex and directrix.

The vertex is

(

–

)

and the directrix is

–

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

(

–

)

with

Solve for the dilation factor

Find the distance between the vertex and the directrix. The directrix

–

is a horizontal line. The distance between a point and a horizontal line is the length of the vertical line segment from the point to the line.

So,

–

Now use

to solve for

Since the parabola opens up,

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

–

Looking for more? Try these:

Lesson: Parabolas

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.1Find the vertex of a parabola

L.12Equations of horizontal and vertical lines

Lesson: Parabolas

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