Question

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?

Answer 1

Answer:

Therefore the maximum height of the diver is 16 feet.

Step-by-step explanation:

The path of a driver is given by

$y=- \frac49 x^2+\frac{24}{9}x +12$

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

It is an equation of parabola.

Here $a = -\frac{4}{9}$  and  $b= \frac{24}{9}$

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 $=-\frac{b}{2a}$

                                                   $=-\frac{\frac{24}{9}}{2.(-\frac{4}9)}$

                                                   $= \frac{24}{8}$

                                                   =3

Putting the value of x in the given equation

$y=-\frac{4}{9}(3)^2+\frac{24}{9}.3+12$

  = - 4+8+12

  =16

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

Therefore the maximum height of the diver is 16 feet.