How do you find the domain and range of the function #y = −2x^2 − 6x + 1# without graphing?
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
Use the quadratic formula with
This will give real numbers for
The range is all reals less than or equal to
Complete the square:
(If I knew how, I'd leave some space between "
Now for every real value for
Finally, for all real
The range is