I am having trouble understanding domians and ranges of quadratic equations. I know what domains and ranges are, I just don'tknow about them in terms of quadratics.
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.

Question

I am having trouble understanding domians and ranges of quadratic equations. I know what domains and ranges are, I just don'tknow about them in terms of quadratics. 
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.

kc_kennylau · Answer

Tell Patricia to find a teacher or a tutor to help her understand the concepts

anonymous · Answer

this is a question that i have recieved @kc_kennylau I cant do that

kc_kennylau · Answer

Complete the square first

kc_kennylau · Answer

I need a completed square to explain

anonymous · Answer

?

kc_kennylau · Answer

Have you forgotten how to complete a square?

anonymous · Answer

Iam just starting this unit and I dont know what you mean by that

kc_kennylau · Answer

Do you know how to solve a quadratic equation?

anonymous · Answer

by factoring, yes

kc_kennylau · Answer

Do you know other methods?

anonymous · Answer

not yet no :/

kc_kennylau · Answer

no problem, never mind then

kc_kennylau · Answer

completing the square will make your equation in the form of a(x+b)^2+c

anonymous · Answer

In general, Domain is any possible x values that would work for a given function. 

For example if you have y = square root of x You need to know if they want integers or real numbers. I'm going to say real numbers here. The domain would be the set of any real numbers that are greater than or equal to 0. We can't have negative numbers under a square root sign so we don't include them in the domain. 

So now that we have our x values clear in our mind, the Range of that function would be the set of all possible y values that could be produced by using those x values in the domain. So the Range of y = square root of x would be the set of all real numbers greater than or equal to 0. Next post will be about quadratics.

anonymous · Answer

For your question, you need to try to picture what the quadratic looks like.  Does it open upward or downward?  Your equation opens downward because there's a  minus sign in front of the x^2.

anonymous · Answer

So it looks like a mountain (instead of a big bowl).  We need to know where the vertex is (the peak of the mountain). The easiest way to figure that out is to complete the square.  Review how to do that so you know how.  Also review how the equation is set up to tell you the co-ordinates of the vertex.
y = −x2 + 4x − 21 = - (x^2 - 4x + 21) = - (x-2)^2 -17
This tells us that the vertex is at (2, -17).   There are no x values that wouldn't work.  So all possible real numbers can be used as x values.  The domain is the set of all real numbers.  

But for the range, the y values would only be starting at -17 (the top of the mountain) and getting more and more negative.  So the range is real numbers that are less than or equal to -17.