Expert: Scott A Wilson - 1/25/2010

Question
How can i graph this function F(x)= 2-x^2 , using the elementary precalculus curve sketching techniques? I know how the function looks like, but i can sketch it, i got its symmetric twice, and it's wrong, so plz step by step using these techniques, how can i get it ?

Answer
The function is a maximum where x is 0.  That means on the y axis, the value is 2.
It is a parabola that crosses the x axis at ±√2.  The slope at x=0 is 0.

The more x increases, the slope gets more and more negative.
The more x decreases, the slope gets more and more positive.