Indicate the equation of the given line in standard form.
the line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).

0.5x+y=0.5

Use the two points to find the slope. X changes by 4 while y changes by -2 so the slope is -.5. Then put it in point slope form. We'll use the point 1,0. So y-0=-0.5(x-1). Simplify it down to y=-0.5x+0.5 then carry over the x to the other side to 0.5x+y=0.5. That's how I did it, but there's probably a more efficient way to do it.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

it could be 1,3 and more others to create a cylinder.

step-by-step explanation: