Help me please :(
Find the points where the line x + 2y = 4 cuts the parabola y = (x − 1)^2, and show that
the line is the normal to the curve at one of these points.

Question

Help me please :( 
Find the points where the line x + 2y = 4 cuts the parabola y = (x − 1)^2, and show that
the line is the normal to the curve at one of these points.

anonymous · Answer

Okie dokie, what is the definition of a line being normal to a curve?  Write it out here so as to get everyone on the same page

aonz · Answer

when m1 m2 = -1?

aonz · Answer

where m1 and m2 are gradients?

anonymous · Answer

What's the gradient of each curve?

aonz · Answer

its 2x-2 and - 1/2

anonymous · Answer

2x-2 is the gradient of (x-1)^2 in general, but what is the gradient of the curve at the point of intersection?

aonz · Answer

gradient is 2

anonymous · Answer

Good, now we just need to verify that 
$$m _{1}m _{2} = -1$$
Let us define
$$m_{1} = 2$$ and
$$m _{2}=-\frac{ 1 }{ 2 }$$
Take it from there

whpalmer4 · Answer

The line intersects the parabola at (2,1) and at (-1/2,9/4).  The former is the one where it is normal to the curve.

aonz · Answer

ok.. so the -1/2 is the one that is the normal?

whpalmer4 · Answer

Former is the earlier one, latter is the later one