How do you graph the inequality y≤−x2−3x+10?

1 Answer
Andy Y.
May 19, 2017

Shade under the parabola.

Explanation:

First, graph the parabola y=−x2−3x+10. If you complete the square, you can rewrite this in vertex form giving you
y=−(x2+3x+94−94−10)
y=−((x+32)2−494)
y=−(x+32)2+494

So the parabola opens downward and has a vertex at
(−32,494)=(−15,12.25)

The y intercept occurs when x=0, giving (0,10)

The x intercept occurs when y=0, giving (2,0) and (−5,0)

Finally, if your y values are less than the parabola, simply shade underneath the parabola. The graph would look like this:
enter image source here

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