Question

Which is one of the transformations applied to the graph of f(x)= x2 to produce the graph of p(x)= -50+14x-x2

Answer 1

Let's find the coordinates of parabola vertex:
$x_v= \frac{-b}{2a} =- \frac{14}{2\cdot(-1)} =7 \\ y_v=-50+14\cdot 7-7^2=-50+98-49=-1$, so the vertex is placed at point (7,-1).
Since in the equation $p(x)=-50+14x-x^2$ the member $x^{2}$ is with minus sign, then you should do such transformation with graph of function $f(x)= x^{2}$:
1. Reflect graph about the x-axis;
2. Translate reflected graph 7 units right and 1 unit down.