Hi could you please help me with this question:

The straight line with the equation x+y-3=0 is the normal to the parabola with equation
y=x^2-x+2 at the point where x is equal to
a)-1
b)0
c)1
d)2
e)3

I don't know how to solve this algerbratically.

I assume you know that normal means perpendicular.
the line you give has some slope, m. you need to know where this slope is perpendicular to the parabola. In other words, you need to find out where the slope of the parabola is is -1/m. I assume you know how to get the equation for the slope of the parabola at each point. Just use that and solve for x when the slope is -1/m. make sense?

I have verified that the correct answer is among those you've listed. Let us know if you need more help and please show your own work so we know what you've gotten.

The following Web site should explain it all to you:

Tangents and Normals