Given the equation of the parabola:
where: y is the height of a certain firework in the air
and, x is the number of seconds after the fuse is lit
We will find the following:
1) Graph the function
To graph the function, we will assume suitable values for x and find the corresponding values of y
So, we will make a table between x and y
The table and the graph of the function will be as shown in the following picture:
2) What are the zeros of the function?
The zeros of the function are the points of intersection with the x-axis
As shown in the graph of the function:
The zeros are: (3, 0) and (13, 0)
3) The firework will explode when it reaches its highest point.
As shown the highest point is = (8, 400)
so, the fireworks will explode after 8 seconds after the fuse is lit.
The highest of the firework will be = 400 feet
4) What is the meaning of the zeros of the function?
There are two zeros:
The first (3, 0): means the firework will start to fly over the ground after 3 seconds of the fuse lit
The second (13,0): means the firework will return to the ground after 13 seconds of the fuse lit