"Find the point(s) on the parabola

at which the normal line passes through the point (2,0). Illustrate by graphing the parabola and the normal line(s)."

I started off by finding

which would be the slope of a tangent line at x.

Next, I assumed the negative reciprocal

is the slope of the normal line.

*** Here's the problem: the tangent line's slope is simply 2, so its reciprocal is only -1/2 and not all the mess you wrote!

Remember: slope is a number.

Tonio

Then, using the given point:

But when I use the quadratic formula I get:

or

which appears to be a problem. I must have messed up somewhere...

Any help with solving this problem is appreciated.