Graph the system of inequalities...

Question

ammarah · Answer

$$y \le-x ^{2}                                      $$

ammarah · Answer

$$y >x ^{2}-4$$

ammarah · Answer

These are the two system of inequalities^^^

ammarah · Answer

@Mertsj @Mr.ClayLordMath

mertsj · Answer

Graph:
$$ y = - x^2$$
Draw a solid line.  
Shade the inside of the parabola

mertsj · Answer

Graph:
$$y=x^2-4$$
Make it dotted.
Shade the inside of the parabola

ammarah · Answer

i know but im having trouble graphing....

ammarah · Answer

do i like find the vertex first??

ammarah · Answer

@mathstudent55

mertsj · Answer

Just get some ordered pairs.  You know they are parabolas so get 3 ordered pairs and use symmetry.  If you know how to find the vertex, that would be helpful.

ammarah · Answer

my graph is turning out weird......how do i graphhh???@mathstudent55

ammarah · Answer

@mathstudent55 @Easyaspi314

anonymous · Answer

Ammarah...what's the question? Or is everything clear now?

ammarah · Answer

the question i posted above.....how do i graph iottt

ammarah · Answer

noo one is helping me....and this site is lagging so myuchh

anonymous · Answer

you there?

ammarah · Answer

yes

ammarah · Answer

i still need a lot of help what is wrong with this site...

anonymous · Answer

I will try helping you with one of the inequalities........

I will take the second one, y > x^2 - 4

anonymous · Answer

Before we graph anything, you must realize that the graph itself will be dotted becuase we do not want when y = x^2 - 4, we want the graph of y > x^2 - 4.

anonymous · Answer

Now, the graph of y = x^2 - 4 (which will be dotted), is simply a parabola.....it has x-intercepts of x = 2 and x = -2, and it is U-shaped.

anonymous · Answer

It will look look like this...........

anonymous · Answer

|dw:1382332605265:dw|

anonymous · Answer

Now...we want where y > x^2 -4...so the only question remains is WHERE to shade...inside or outside the parabola..........

anonymous · Answer

The simplest way to determine that...is to take ANY point, say (0,1)...and see whether (0,1) makes the inequality y > x^2 - 4 true or false...


let's substitute x = 0 and y = 1,

is 1 > (0)^2 - 4
Is 1 > 0 - 4
Is 1 > -4

Answer is YES!

Therefore we shade where (0,1) is..that is INSIDE the parabola..

therefore, the graph of y > x^2 - 4 will look like.........

anonymous · Answer

|dw:1382332824812:dw|

anonymous · Answer

Does this makes sense??????

anonymous · Answer

well?

ammarah · Answer

yes but im confused on the first inequality

anonymous · Answer

well, I helped you with the second one. Your welcome!