IXL - Domain and range of quadratic functions: equations (Algebra 2 practice)

What is the range of this quadratic function?

–

{

≤

}

{

≥

}

{

≥

–

}

all real numbers

ref_doc_title.

Learn with an example

question

What is the range of this quadratic function?

–

{

≥

–

}

{

≥

}

{

≥

}

all real numbers

key idea

The range of a function is the set of all

y-values

that are outputs of the function.

solution

The graph of the function

–

is a parabola. To find the range of the function, find the

-coordinate

of the parabola's vertex.

One way to find the vertex is to rewrite the function in vertex form:

(

–

)

You can do this by completing the square.

–

Add and subtract

(

–

)

–

Add and subtract

–

Group terms to make a perfect square

–

Group terms to make a perfect square

Simplify

(

–

)

–

Simplify

Factor the perfect square

(

–

)

–

Factor the perfect square

Now the function is in vertex form. Since

the parabola opens upward. Since

and

–

the vertex is at

(

–

)

The range is the set of

y-values

that are outputs of the function, so the range is all real numbers greater than or equal to

–

the

y-coordinate

of the vertex. In set-builder notation, the range is written like this:

{

≥

–

}

You can also find the vertex of a quadratic function by first finding the

-intercepts.

This works well for the function

–

since it can be factored as

(

–

)

(

)

This tells you that the function's

x-intercepts

are at 6 and

–

The vertex of a quadratic function is on the parabola's axis of symmetry, which is the vertical line halfway between the

x-intercepts.

For this parabola, the axis of symmetry is

Now find the

y-coordinate

of the vertex by evaluating the function at

–

(

)

–

(

)

–

So, the parabola has a minimum at

(

–

)

and opens upward.

Again, you can see that the range is all real numbers greater than or equal to

–

{

≥

–

}

Looking for more? Try these:

Lesson: Quadratic functions

Lesson: Completing the square

Lesson: Factoring quadratic equations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

N.8Domain and range of quadratic functions: graphs

N.6Write a quadratic function in vertex form

M.5Factor quadratics

Lesson: Quadratic functions

Lesson: Completing the square

Lesson: Factoring quadratic equations

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