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

Aug 31, 2017

Start by graphing the function:

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

The ${x}^{2}$ coefficient is negative so we have $\cap$ shaped parabola. The roots ate given by:

$- {x}^{2} - 7 x + 10 = 0 \implies {x}^{2} + 7 x - 10 = 0$

which using the quadratic equation gives :

$x = - \frac{7}{2} \pm \frac{\sqrt{89}}{2}$

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]}