The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

Set-Builder Notation:

Rewrite the equation in vertex form.

Complete the square for .

Use the form , to find the values of , , and .

Consider the vertex form of a parabola.

Substitute the values of and into the formula .

Multiply by .

Find the value of using the formula .

Simplify each term.

Raise to the power of .

Multiply by .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

Move the negative in front of the fraction.

Substitute the values of , , and into the vertex form .

Set equal to the new right side.

Use the vertex form, , to determine the values of , , and .

Since the value of is positive, the parabola opens up.

Opens Up

Find the vertex .

The range of a parabola that opens up starts at its vertex and extends to infinity.

Interval Notation:

Set-Builder Notation:

Determine the domain and range.

Domain:

Range:

Find the Domain and Range f(x)=2x^2-7x-4