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

In summary, the conversation discusses how to sketch the graphs of y = |x| and y = 2 - x^2 on the same axis and determine the values of x where the inequality |x| < 2 - x^2 is true. The process involves finding the points of intersection between the two graphs and plugging in |x| in the equation y = 2 - x^2.
  • #1
uniidiot
24
0

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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  • #2
for which values of x is the graph of y = |x| under the graph of y = 2 - x^2 ?
 
  • #3
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
 
  • #4
you first draw graphs, then find the points of intersection for the relevant places.
 
  • #5
ok, but how?? :S
 
  • #6
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...
 
Last edited:

1. What is the shape of the curve y = |x|?

The curve y = |x| is a V-shaped curve that passes through the origin and has a slope of 1 on either side of the origin.

2. How does the graph of y = 2 - x^2 compare to the graph of y = |x|?

The graph of y = 2 - x^2 is a parabola that opens downwards and intersects the x-axis at (0,2). It is symmetric about the y-axis. The graph of y = |x| is a V-shaped curve that is symmetric about the origin.

3. Are there any points of intersection between the curves y = |x| and y = 2 - x^2?

Yes, there are two points of intersection between the two curves. One is at (0,2) and the other is at approximately (-1.41, 1.41).

4. How do you find the x-intercepts of the curve y = |x|?

The x-intercepts of the curve y = |x| can be found by setting y = 0 and solving for x. This will give us two solutions, x = 0 and x = -0.

5. What is the maximum value of y for the curve y = 2 - x^2?

The maximum value of y for the curve y = 2 - x^2 is 2, which occurs at the x-coordinate of 0.

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