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

AI Thread Summary
The discussion focuses on sketching the graphs of y = |x| and y = 2 - x^2 on the same axis. Participants clarify that y = |x| forms a V-shape, while y = 2 - x^2 is an inverted parabola with its vertex at (0, 2). The main question revolves around determining the values of x for which the inequality |x| < 2 - x^2 holds true. To find these values, one must identify the points of intersection by setting |x| equal to 2 - x^2 for both positive and negative x. The solution involves solving the resulting equations to find the regions where the inequality is satisfied.
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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


Homework Equations





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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for which values of x is the graph of y = |x| under the graph of y = 2 - x^2 ?
 
is that what its asking?

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
 
you first draw graphs, then find the points of intersection for the relevant places.
 
ok, but how?? :S
 
if you have drawn the graphs you just 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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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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