Graph the quadratic function f(x)= -2x^2 + 6x - 2

  see below for a graph

Step-by-step explanation:

The function can be rewritten to vertex form to aid in graphing.

  f(x) = -2(x^2 -3x) -2

  f(x) = -2(x^2 -3x + 2.25) -2 +4.50 . . . . . . add (3/2)^2 inside parentheses and subtract an equivalent amount outside parentheses

  f(x) = -2(x -1.5)^2 +2.5

The vertex is located at (1.5, 2.5), and the vertical scale factor is -2. The point (3, -2) will be another point on the graph, along with the y-intercept (0, -2) and the vertex (1.5, 2.5).