Question

A diver jumps from a platform, and the height of their dive is modeled by the equation Y= -4/9x²+24/9x+9 where x reprents time. What is the maximum height of the diver?

a. 9 ft
b. 12 ft
c. 15 ft
d. 18 ft

Answer 1

The maximum height of the diver is 12 ft.

Step-by-step explanation:

To find the maximum height of the diver, we need to determine the vertex of the quadratic equation Y= -4/9x²+24/9x+9. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -4/9 and b = 24/9. Plugging in these values, we get x = -24 / (2(-4/9)), which simplifies to x = 3.

Now we can substitute the value of x into the equation to find the maximum height. Plugging x = 3 into Y = -4/9x²+24/9x+9, we get Y = -4/9(3)²+24/9(3)+9. Simplifying this expression, we find Y = 12, so the maximum height of the diver is 12 ft.