Question

The path of a ball thrown can be modeled by the equation f(x)=−16x^2+45x+6, where x is the horizontal distance. Use a transformation to create a new model in which the ball is thrown twice as far. What is the new equation, what is the transformation, and how did you pick this?

Answer 1

g(x) = -4x^2 +(45/2)x +6

Explanation:

A function is scaled horizontally by replacing x with x/k, where k is the expansion factor. Here, we want to expand the graph horizontally by a factor of 2, so the new function will be f(x/2).

g(x) = f(x/2) = -16(x/2)^2 +45(x/2) +6

g(x) = -4x^2 +(45/2)x +6