Need help knowing where to shade and why

Question

4x² − y − 2 > 0

 

I have already graphed the parabola, but I can't seem to figure out where to shade the graph. 

Answer 1

So your parabola looks like:

y < 4x² - 2

 

Let's try putting 0 into x:

y < 4 * 0 - 2

y <  0 - 2

y <  -2

 

Similarly (having x = 1):

y < 4 * 1 - 2

y < 4 - 2

y < 2

So you would have to shade underneath/outside of the parabola as the answers have to be less than the offered x. Don't forget, as we're using a less than sign here, your parabola should be dashed instead of a full-and-complete line.

 

Answer 2

First, lets check to see if you graphed the parabola correctly.  Solve for y from the given inequality.

 

-y > -4x² + 2

 

 y < 4x² - 2

 

 

So you will end up with parabola with a y-intercept of (0, -2) and vertical stretch of 4.  If you have this parabola, just shade the region in the coordinate systems that is below the parabola.  Also, the parabola is a dashed curve, rather than a solid curve.  You only have solid curve when it is "equal to".