Find the length of AB.

Ok:

Step-by-step explanation:

So these triangles are similar. That means that the ration between their sides are the same. In this case, we have then:

AC/CB = CE/CD. Or AC/3 = 16/4.

We can solve AC to be 12. To find AB, it is AC-3 which is 9.

So AB=9

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

step-by-step explanation: