How do you graph the inequality #y>=x^2+3x-18#?

1 Answer
Dec 26, 2016

Answer:

It is the region comprising the parabola #x+3/2)^2=y+81/4# and its interior. See the illustrative Socratic graph.

Explanation:

The boundary for the region that comprises point ( x, y ) such that

#y>= x^2+3x-18# is the parabola #y = x^2+3x-18#

This has the form #(x+3/2)^2=y+81/4# disclosing that the vertex of

the parabola is #(-3/2, -81/4)# and its axis is #x = -3/2 uarr#.

If (x, y) is on the parabola, for any interior point (x, Y), #Y >=y#.

graph{y-x^2-3x+9>=0 [-40, 40, -20, 20]}