Question

What parent function has the following applications: profit, gravity, and calculating area?

Answer 1

Answer:

Suppose that you have a square of side length x, the area of this square will be:

A = x^2.

Now, by dynamics, we know that the position of an object that is falling down from a height H, can be written as:

H(t) = (-g/2)*t^2 + H.

We can see a pattern, x^2 is used in both.

Now, profit can be also modeled with quadratic equations, where our objective is to find the maximum of the quadratic (so we can have the maximum profit)

Then the parent function that is useful for gravity, calculating area and profit is the quadratic function:

f(x) = x^2