At What point does the normal

(1 pt) At what point does the normal to y= 5-2x+2x^2 at (1,5) intersect the parabola a second time?
( , )

The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are negative reciprocals -- i.e. if the slope of the first line is then the slope of the second line is m/-1

y= 5-2x+2x^2
Taking the derivative of y,
y' = -2x + 4x
The slope of the tangent at (1,5) is
y' = -2(1) + 4(1) = 2
Thus the normal will have a slope of -1/2 and the line equation as
y = (-1/2)x + b
At (1,5),
5 = (-1/2)(1) + b
b = 11/2
Thus the equation of the normal is y = -(1/2)x + 11/2

Now you can find the intersection of
y= 5-2x+2x^2 and y = -(1/2)x + 11/2

The answer should be (-1/4, 45/8).