Question

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

Answer 1

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]}