Question

the path of a diver is modeled by the function f(x) = -9x^2+9x+1 where f(x) is the height of the diver above the water and d is the horizontal from the end of the diving bored

1. Tryphena
Key points in the divers path that has a model of f(x) = -9•x² + 9•x + 1 are;
• Maximum height reached ≈ 3.28 units
• Height of the board = 1 unit distance
• Maximum horizontal distance reached is approximately 1.101 unit distance

### How can the path of the diver be evaluated?

The given function that models the path of the diver is; f(x) = -9•x² + 9•x + 1
Where;
f(x) = The height reached by the diver above the water
x = The horizontal distance traveled from the diving board
Analyzing the above function gives;
Highest point of the path is given by the coordinates for the peak of a quadratic function are;
• (-b/(2•a), -D/(4•a))
• D = b² – 4•a•c
The x-coordinate of the highest point, d, is therefore;
d = -9/(2×(-9)) = 1/2
D = 9² – 4 × (-9) × 1 = 118
At the highest point, ylh = -118/(4×(-9)) = 59/18 ≈ 3.28
Therefore;
The maximum height reached, h, is therefore;
• h ≈ 3.28 units
The distance from the board at the diver is at maximum height, d ≈ 0.5 unit
The height of the diving board, hd, can be found as follows;
When the diver is at the diving board, x = 0, which gives;
hd = f(0) = -9×0² + 9×0 + 1 = 1
• Height of the diving board, hd = 1 unit distance
Maximum distance reached by the diver before landing in the water is given by the equation;
0 = -9•x² + 9•x + 1
Using a graphing calculator gives;
x ≈ 1.101, or x ≈ -0.101
• The maximum distance reached is approximately 1.101 units