How do you graph the inequality #y<=x^2-4#?

1 Answer
Sep 5, 2017

Answer:

See below

Explanation:

First consider the limiting case: #y = x^2-4#

This is a parabola with a absolute minimum value
(since the coefficient of #x^2 >0#)

Since there is no term in #x#, #y_min = y(o) =-4#

Considering #y = (x+2)(x-2)#

#y# will vave zeros at #x=-2 and x=2#

From the results above, it is possible to graph #y# in the limiting case.

Now, turning to the inequality: #y <= x^2-4#

This may be represented graphically as the entire area of the #xy-#plane that is below and on the limiting case graph. The area that satisifies the inequality is shown shaded below extended to #(-oo, +oo)# on both axes.

graph{y<=x^2-4 [-10, 10, -5, 5]}