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

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:
Locate the vertex of the parabola.
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