Which Inequality region should I shade?

OP

Original post by Physikoi

I have the inequalities f(x) = y > x^2 +4x -12
and g(x) = y > 4 - x^2

I plot both graphs and end up shading inside f(x) but outside g(x)
but the answer in the textbook is to shade just inside g(x). I'm questioning if this is right because I thought you had to shade outside when y > negative quadratic inequality.

somebody help soon, I need to go out and get this done within 10 minutes

Reply 2

UncookedYogurt

6

draw em both, then shade each region seperately, i recommend g(x) first, take your time and figure it out

Reply 3

Original post by Physikoi

I have the inequalities f(x) = y > x^2 +4x -12
and g(x) = y > 4 - x^2

I plot both graphs and end up shading inside f(x) but outside g(x)
but the answer in the textbook is to shade just inside g(x). I'm questioning if this is right because I thought you had to shade outside when y > negative quadratic inequality.

Can you upload an image of the question and answer? The inequalities do not make sense, usually you have something like
4 - x^2 >= 0
and for that inequality, the points satisfying it would be between -2 and 2.

Reply 4

OP

Original post by UncookedYogurt

draw em both, then shade each region seperately, i recommend g(x) first, take your time and figure it out

I did this and most of g(x) is inside the f(x) curve. But which region do i shade?

Reply 5

UncookedYogurt

6

Original post by UncookedYogurt

draw em both, then shade each region seperately, i recommend g(x) first, take your time and figure it out

tbh its been a while since i did this

Reply 6

OP

Original post by mqb2766

Can you upload an image of the question and answer? The inequalities do not make sense, usually you have something like
4 - x^2 >= 0
and for that inequality, the points satisfying it would be between -2 and 2.

I haven't got the textbook infront of me right now but this is what happens when I put it in geogebra.
https://imgur.com/a/9xbC9Wc
but which region is meant to be shaded

Reply 7

Original post by Physikoi

I did this and most of g(x) is inside the f(x) curve. But which region do i shade?

Forgot my previous response.

For f(x), you have roots at -6 and +2, the shaded region is above this. The curve is a bowl.
For g(x), you have roots at +2, -2, the shaded region is above this. The curve is an inverted bowl.

The overall shaded region is the intersection of these two areas

Reply 8

Original post by Physikoi

I haven't got the textbook infront of me right now but this is what happens when I put it in geogebra.
https://imgur.com/a/9xbC9Wc
but which region is meant to be shaded

dark blue.

Reply 9

OP

Original post by mqb2766

dark blue.

Yes I thought so too. But the textbook shaded inside the negative quadratic only. JUST TO clarify, this is the question
https://imgur.com/a/8xyo7RO

and this is the answer:
https://imgur.com/a/GUgovMJ

Reply 10