Find the line that is normal to the parabola at the given point remember that normal means perpendicular perpendicular lines have slopes that multiply to -1 we can use point slope form to write the equation of the line since we are given the point (1,0)
we just need the slope
take derivitive y'=1-2x at x=1 y'=1-2(1) y'=1-2 y'=-1
the slope is -1 the perpendicular of that slope is what number we can multiply to get -1 -1 times what=-1? what=1 duh so point (1,0) and slope 1 y-0=1(x-1) y=x-1 is da equation
solve for where y=x-1 and y=x-x² intersect
set equatl to each other since equal y x-1=x-x² x²-1=0 factor difference of 2 perfect squares (x-1)(x+1)=0 set to zero
x-1=0 x=1 we got this point already
x+1=0 x=-1 sub back y=-1-(-1)² y=-1-(1) y=-1-1 y=-2
