Question

Your friend, Patricia, is having a hard time understanding the concept behind the domain and range of a parabola. Using complete sentences, explain the meaning of the domain and range of the graph of
y = −x2 + 4x − 21 and how to find both. Keep in mind, your goal is to help Patricia understand the "concepts", not just how to use the steps.

Answer 1

Need help with this!

Answer 2

domain relates to the x values and all the possible values that we can use for x that will give us a valid function. So what we need to do is think are there any values of x that if I plug them into my equation they won't give an answer or the answer will be undifined?

Answer 3

Range is all the possible outputs of our function AKA the y values. for all x's that we can plug in what are al the possible y values? Are there values that will never occur?

Answer 4

Oh, okay, thx, do we have to add anything else for the essay?

Answer 5

maybe find the domain and range of the above function

Answer 6

Ok, hmm, from what to what?

Answer 7

Are there any restrictions for x? Any values that will give invalid outputs like 1/0 or squareroot of a negative number?

Answer 8

I don't think so, so maybe I can put values from 1-10

Answer 9

you are right in that all x values will give valid outputs so all values of x are possible therefor our domain is......

Answer 10

\[-\infty <x < \infty \]

Answer 11

range is more difficult. do you have a graphing calculator?

Answer 12

Yep! I have the Texas Instruments one. :)

Answer 13

so graph the equation and find out where y exists and where it doesn't

Answer 14

Yep, just finished, thx for your help, it was much appreciated!

Answer 15

for example if you have the above situation y will never be bigger than 4 so the range would be y<4. Ur welcome