Place Maura's feet at the origin, and determine a few key points on the graph.
Example Solution: y=-4/25(x-5)^2+8 Domain: 0≤ x ≤ 10 Range: 4≤ y≤ 8
Practice makes perfect
The function will look a little different depending on where in the coordinate plane you choose to place the graph. Let's choose Maura's feet to be at the origin. Since the nozzle is 4 feet above the ground, its coordinates will be (0,4).
The top of the flowers is at the same height as the nozzle, but 10 feet to the right.
The highest point is 8 feet off the ground, and since the model that Maura's using is a parabola it's in between the flowers and nozzle, giving it the coordinates (5,8).
This parabola can be described by a quadratic function.
y= a(x-h)^2+k
This is the so-called vertex form of a quadratic function. Here, (h,k) is the vertex, and since the maximum point is (5,8) that gives us h=5 and k=8.
y=a(x-5)^2+8
To find the coefficient a, let's use a point that we know is on the graph, (0,4).
The coefficient is a= - 425, so let's put that in the function.
y= - 425(x-5)^2+8
Domain and Range
What is the domain and range? The domain is what x-values we can substitute into the function. The parabola is a good approximation of the water's journey between the nozzle and the flowers, so we can write a reasonable domain.
0≤ x≤ 10
In this domain, the height of the water varies between 4 and 8 feet including the endpoints. With this information, we can write the range.
4 ≤ y ≤ 8
