Question

find the value of k for which y=2x+k is a normal to y=2x^2-3

the answer should be -87/32

Answer 1

the derivative of [2x^2-3] is 4x. this will give you the slope of the tangent line. since the normal line has slope 2, it has to be perpendicular to the tangent line... so solve: (4x)*(2) = -1 for x...
you should get x=-1/8.
this is the point on the parabola where the tangent line has slope of -1/2 (perpendicular to a slope of 2).
now find the y-coordinate on the parabola when x=-1/8. you should get y=-95/32.

so now, plug these x and y values into y = 2x + k and solve for k.