Let T be a linear transformation from R^3 to R^3 Determine whether or not T is one-to-one in each of the following situations:.
1. Suppose T(0, -2, -4) = u. T(-3,-4,1) = v. T(-3, -5, -3) = u + v.
2. Suppose T(a) = u, T(b) = v. T(c) = u + v. where a, b,c, u,v v are vectors in R^3
3. Suppose T is an onto function
A. T is not a one-to-one function
B. T is a one-to-one function
C. There is not enough information to tell

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