Hi Dear Jiskha team,

Question

I have Algebra homework and I will need some help.
The homework is following:
Suppose you are using a computer to draw a face on a coordinate plane. The eyes are at (–3, 3) and (3, 3). The tip of the nose is at the origin. To make a smiling mouth, you are going to enter the equation for the graph of a quadratic function, with its appropriate domain.

Post the quadratic function that you would use (in any form) with the domain. Explain how you determined your equation and why you wrote it in the form that you did.

Thanks in advance!

Answer 1

Draw the given items on your calculator or a piece of graph paper.
A quadratic centred on the y-axis has the formula y=x^2+k where k is the displacement from the origin (up:k>0, down:k<0).
The above quadratic is a smiley. If you want a sad face, it's y=-x^2+k.

If you find that the face smiles too much, you can try y=0.5x^2+k, etc.

The domain gives the extent of the mouth, such as from -2 to +2.

Here're some examples where the domain is not specified.

http://img138.imageshack.us/img138/7217/1329904502.png
http://img141.imageshack.us/img141/7217/1329904502.png