# Sketch the curves y =|x| and y = 2 - x^2 on the graphs

#### uniidiot

1. Homework Statement
Sketch on the same axis the graphs of y = |x| and y = 2 - x^2.

For which values f x is the inequality |x| < 2 - x^2

2. Homework Equations

3. The Attempt at a Solution

I don't really understand what it is asking me to do, i've sketched the two curves, y = |x| 45 degrees from the x axis and at -45 degrees from the x axis, and the curve y = 2 - x^2 is an upside down quadratic curve with the vertex at -2 y.

thanks

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#### malawi_glenn

Homework Helper
for which values of x is the graph of y = |x| under the graph of y = 2 - x^2 ?

#### uniidiot

if so how do i work that out, is it similar to the wa you work out whether a curve crosses the x-axis.

thanks

#### malawi_glenn

Homework Helper
you first draw graphs, then find the points of intersection for the relevant places.

ok, but how?? :S

#### malawi_glenn

Homework Helper
if you have drawn the graphs you jsut plug in |x| in the y = 2 - x^2

so we get:

x = 2 - x^2, for x > 0

and

-x = 2 - x^2, for x < 0

points of intersection is where the two graphs/functions are equal...

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