How do you graph the inequality #y>=x^2-10x+25#?

1 Answer


See below:


Let's first graph the parabola, then figure out what needs to be shaded.

We can set the LH to 0 and factor the RH:

#0=(x-5)^2=> x=5#

This graphs out to:


Let's now talk about the inequality portion of the question. With #y>=x^2-10x+25#, let's see if the origin is part of the solution:

#0>=0^2-10(0)+25=>0>=25 color(white)(000)color(red)(X)#

The origin is not part of the solution, so we want to shade "inside the bowl".

The line of the parabola will be solid to show that it is part of the solution.