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

Answers

Key points in the diverspath 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 distancetraveled 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

diverspaththat has amodelof f(x) = -9•x² + 9•x + 1 are;## How can the path of the diver be evaluated?

functionthat models the path of the diver is; f(x) =-9•x² + 9•x + 1heightreached by thediverabove thewaterhorizontal distancetraveledfrom the diving boardcoordinatesfor thepeakof aquadraticfunction are;b² – 4•a•cx-coordinateof the highest point,d, is therefore;1/2118ylh3.28h, is therefore;d≈ 0.5 unitheightof thediving board, hd, can be found as follows;x= 0, which gives;1wateris given by the equation;1.101, or x ≈ -0.101quadraticfunctions here: