How do you graph the inequality $y>=-x^2-7x+10$ ?

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Answer 1 · 2017-08-31T18:04:51

Start by graphing the function:

$y=-x^2-7x+10$

The $x^2$ coefficient is negative so we have $nn$ shaped parabola. The roots ate given by:

$-x^2-7x+10 = 0 => x^2+7x-10 = 0$

which using the quadratic equation gives :

$x= - 7/2 +- sqrt(89)/2$

So we can can graph the quadratic as follows:

graph{y=-x^2-7x+10 [-20, 15, -20, 40]}

Then the required region is simply that outside the quadratic, as follows
graph{y>=-x^2-7x+10 [-20, 15, -20, 40]}

How do you graph the inequality y>=-x^2-7x+10y>=-x^2-7x+10?