The path of the diver is given by y= 4/9 x^2+24/9 x+12where y is the height in feet and x is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?

Therefore the maximum height of the diver is 16 feet.

Step-by-step explanation:

The path of a driver is given by

where y is the height in feet and x is the horizontal distance.

It is an equation of parabola.

Here  and  

Since a<0 then the open side of the parabola is in downwards direction.

The maximum height of the driver is the y-coordinate of vertex the parabola.

The x-coordinate of the vertex

                                                   =3

Putting the value of x in the given equation

  = - 4+8+12

  =16

Therefore the coordinate of the vertex is = (3,16)

Therefore the maximum height of the diver is 16 feet.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.