THREE LINEAR EQUATIONS WITH THREE VARIABLES

Question

A ball is tossed into the air so that the height after
1, 3, and 6 seconds is as given in the following table. If the relationship between the height of the ball
h and the time t is quadratic, then the relationship can be written as:
h=at^2+bt+c.

 

TABLE OF TIME TO HEIGHT :

1 second time = 240 in height.

3 second time = 240 in height.

6 second time = 0 height.

How to use the information in the table to write a system of three equations in three variables a, b, c?

How to solve the system to find the exact relationship between h and t?

So with the above information how do I set up a system of three linear equations to find the answer? Please help.

Answer 1

We know the equation to be that of an upside down parabola.  By symmetry, the equal heights 240 ft at t= both 1 & 3 seconds tells us that the axis of symmetry is t=2.

 

You have three points (t,h(t)):  (1,240)  (3,240)   (6,0)

Using these points, substitute for t & h, to get three equations--the unknowns are now a, b, c!

Solve that system...carefully...perhaps by using Cramer's Rule--any valid method will do. (Note that any two equations can be subtracted, to eliminate c, so you could easily reduce this to two equations in unknowns a & b.)