Answers

1. 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

   Learn more about quadratic functions here:

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