Question

You take measurements of the distance traveled by an object that is increasing its speed at a constant rate. The distance traveled d as a function of time t can be modeled by a quadratic function. What is the quadratic function that models distances of 21 ft at 1 s, 59 ft at 2 s, and 141 ft at 4 s?

Answer 1

Follows are the solution to this question:

Explanation:

Given:

`s_1 = 21 \ \ t_1 = 1\\\\s_2 = 59 \ \ t_2 = 2\\\\s_3 = 141 \ \ t_3 = 4`

All points are on the graph including its quadratic function, in order to install their coordinates to values of x and y with the following values:

`y= ax^2 + bx + c\\\\21=a+b+c` Inserting the coordinates of the first point

`y= ax^2 + bx + c\\\\59 =4a+2b+c` Inserting the coordinates of the second point

`y= ax^2 + bx + c\\\\141=16a+4b+c` Inserting the coordinates of the third point