Question

NO LINKS!! Please help me with this statement Part 1mm​

Answer 1

15 feet

Explanation:

Given quadratic function:

`f(x)=-(4)/(9)x^2+(24)/(9)x+11`

where f(x) is the height (in feet) and x is the horizontal distance (in feet) from the end of the diving board.

The maximum height of the diver is the y-value of the vertex (h, k) of the function.

`\boxed{h=-(b)/(2a) \quad \quad k=f(h)}`

where f(x) = ax² + bx + c

From inspection of the function:

`a=-(4)/(9) \quad b=(24)/(9) \quad c=11`

Substitute the values of a and b into the formula for h to find the x-value of the vertex:

`\implies h=-((24)/(9))/(2\left(-(4)/(9)\right))`

`\implies h=((24)/(9))/((8)/(9))`

`\implies h=(24)/(8)`

`\implies h=3`

Substitute this into the function to find the y-value of the vertex, and therefore the maximum height of the diver:

`\begin{aligned}\implies k=f(3)&=-(4)/(9)(3)^2+(24)/(9)(3)+11\\&=-4+8+11\\&=15 \end{aligned}`

Therefore, the maximum height of the diver is 15 feet.

Answer 2

• The maximum height is 15 ft

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Given is the quadratic equation with:

• a = - 4/9, b = 24/9, c = 11

Since a < 0, the graph opens down and the vertex is its maximum point.

The x-coordinate of the vertex is x = - b : 2a:

• x = - 24/9 : 2(-4/9) = -24 / - 8 = 3

Find the value of f at x = 3:

• f(3) = - 4/9*(3²) + 24/9*(3) + 11 = - 4 + 8 + 11 = 15