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 directrix

Simplify any fractions.

key idea

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 directrix

Since the directrix is above the vertex, the parabola opens down. 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 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 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

–

Looking for more? Try these:

Lesson: Quadratic functions

Lesson: Parabolas

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Z.4Write equations of parabolas in vertex form from graphs

Lesson: Quadratic functions

Lesson: Parabolas

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