How do you graph the inequality y>=x^2+3x-18y≥x2+3x−18?

1 Answer
A. S. Adikesavan
Dec 26, 2016

It is the region comprising the parabola x+3/2)^2=y+81/4x+32)2=y+814 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-18y≥x2+3x−18 is the parabola y = x^2+3x-18y=x2+3x−18

This has the form (x+3/2)^2=y+81/4(x+32)2=y+814 disclosing that the vertex of

the parabola is (-3/2, -81/4)(−32,−814) and its axis is x = -3/2 uarrx=−32↑⏐ ⏐⏐.

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

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

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