IXL - Find properties of a parabola from equations in general form (Geometry practice)

What is the vertex of the parabola

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Learn with an example

question

What is the vertex of the parabola

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key idea

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 vertex form of a parabola that opens right or left is

(

–

)

The vertex is

(

)

the parabola opens right. If

the parabola opens left.

To complete the square for the quadratic

add and subtract

group terms, and factor.

Adding and subtracting

(

)

preserves the equality

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Adding and subtracting

preserves the equality

Group terms to make a perfect square

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Group terms to make a perfect square

Factor the perfect square

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Factor the perfect square

solution

To find the vertex, write the equation in vertex form.

Write the equation in vertex form.

Complete the square and simplify.

–

(

–

)

–

Factor out

–

from the

-terms

–

(

–

)

–

Factor out

–

from the

-terms

–

Group terms to make a perfect square

–

Group terms to make a perfect square

–

(

–

)

Factor the perfect square

–

(

–

)

Factor the perfect square

Identify the vertex.

–

(

–

)

–

(

–

)

Its vertex is

(

)

Looking for more? Try these:

Lesson: Parabolas

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Z.7Convert equations of parabolas from general to vertex form

Z.2Find the focus or directrix of a parabola

Z.1Find the vertex of a parabola

Lesson: Parabolas

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