IXL - Write equations of parabolas in vertex form using properties (Geometry practice)

Write the equation in vertex form for the parabola with vertex

(

)

and focus

(

)

Simplify any fractions.

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question

Write the equation in vertex form for the parabola with vertex

(

)

and focus

(

)

Simplify any fractions.

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, determine which way it opens. Then, solve for the dilation factor

Finally, plug in the vertex coordinates and the dilation factor

Determine which way the parabola opens.

Look at the vertex

(

)

and the focus

(

)

Since the focus is above the vertex, the parabola opens up. So, the parabola 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 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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Z.4Write equations of parabolas in vertex form from graphs

Lesson: Parabolas

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