What is the slope of the line that passes through the points (1,7),
(10, 1)?
3/2
2/3
-3/2
-2/3

The slope of a line is the change in y divided by the change in x.

( y1 - y2 ) / ( x1 - x2 )

It does not matter which point you choose as (x1, y1) and (x2,y2)

( 7 - 1 ) / ( 1 - 10 )

( 6 ) / ( -9 ) This will simplify to -2/3.

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