Consider the path of the water as you make a graph of the parabola, and write the equation in factored form.
Function: y=- 172x(x-120)
Domain: 0≤ x ≤ 120
Range: 0≤ y ≤ 50 Diagram:
Practice makes perfect
There are a few things we know about the parabola that will help us model a graph showing the water's path through the air. If we let the parabola intersect the y-axis at the origin, we know that its second x-intercept must be 120 units to the right of this.
This is enough information to write the quadratic function in factored form.
y=ax(x-120)We also need to find a. The maximum height of the parabola is 50 feet above the barrel of the water cannon. Since the parabola is symmetric about its vertex, we know that the maximum height will be in the middle of the x-intercepts at x=60.
To find the value of a, we have to substitute the vertex into the function and solve for a.
To determine the domain and range, we have to think about the situation. The domain shows all possible x-values of the function. Since the parabola starts at the origin and ends when the water hits the flames 120 feet away, the domain goes from 0 to 120.
0≤ x ≤ 120
As for the range, the water beam cannot go below the flames or the water cannon. This means it is limited to non-negative values of y. Also, it cannot go above its maximum height meaning it has a maximum value that is less than or equal to 50.
0≤ y ≤ 50
