What is the shape of the function y 16x x2?

Restate the question: What is the shape of the function y = 16x - x2?

Since the function highest power is a square, this is a quadratic function, and the graph is a parabola. Maybe that's all you wanted to know, but here's the rest of the story:

Since the coefficient of x is negative (it's -1), the parabola opens down (the shape is an upside down 'u').

The x-intercepts are found by factoring and solving: 16x-x2 = 0 -> x(16-x) = 0 -> x=0 or [16-x=0 -> 16=x]. The graph crosses the x-axis at 0 and 16.

The top of the parabola will be where x=8 (half-way between the intercepts). Substitute in y = 16x - x2 = 16(8) - (8)2 = 128 - 64 = 64.

The graph passes through (0,0), (8, 64), and (16,0).