# How do you find the domain and range of the function #y = −2x^2 − 6x + 1# without graphing?

##### 2 Answers

For the domain, I ask myself what real numbers I could use for

The domain is all real numbers.

To find the range (without thinking about the graph) I need to know what real numbers could I use for

To do that, I'll sole the equation for

Solve for

Use the quadratic formula with

This will give real numbers for

The range is all reals less than or equal to

The interval

Complete the square:

(If I knew how, I'd leave some space between "

Now for every real value for

Furthermore, for

Finally, for all real

The range is