IXL - Write a quadratic function in vertex form (Algebra 2 practice)

The equation of a parabola is

Write the equation in vertex form.

Write any numbers as integers or simplified proper or improper fractions.

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question

The equation of a parabola is

–

Write the equation in vertex form.

Write any numbers as integers or simplified proper or improper fractions.

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

–

Group terms to make a perfect square

–

Factor the perfect square

solution

To write the equation in vertex form, isolate the term in

If the resulting quadratic in

is a perfect square, factor it. Otherwise, complete the square.

Isolate the term in

The term in

is already isolated.

–

Factor or complete the square (depending on the quadratic).

The quadratic

–

is not a perfect square because the constant coefficient is not the square of half the linear coefficient,

≠

–

Complete the square.

–

(

–

)

–

Group terms to make a perfect square

(

–

)

(

–

)

Factor the perfect square

Write the equation in vertex form.

The equation of the parabola in vertex form is

(

–

)

Looking for more? Try these:

Lesson: Quadratic functions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

O.4Complete the square

N.5Graph a quadratic function

Lesson: Quadratic functions

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