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

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.

anonymous · Answer

The domain is all the possible x values that exist in the graph. On the graph -x^2 +4x-21, no matter which  x value you choose, there is a corresponding y value. Even if your x is infinity, negative infinity, or zero, the parabola exists there, so your domain is "all real numbers."

anonymous · Answer

thank you so so so much but i need the range too

anonymous · Answer

The range is all the possible y values. In the above said parabola, the highest is ever reaches is -17. The graph just doesn't exist higher than that. So the range is "all real numbers less than or equal to -17."

anonymous · Answer

*highest it ever reaches*, sorry