Respuesta :
Answer:
132.25 feet
Step-by-step explanation:
Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.
The general form for a quadratic equation is ax² + bx + c,
here a is -16, and b is 92
To find the x coordinate of the vertex, use x = -b/(2a)
We have x = -92/[2(-16)]
x = -92/-32
x= 23/8
Now plug that into the equation to find the y value, which will be the height...
y = 92(23/8) - 16(23/8)²
y = 2116/8 - 16(529/64)
y = 1058/4 - 529/4
y = 529/4
y = 132.25
The maximum height that the ball will reach : 132.25 ft
Further explanation
Quadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
f (x) = ax² + bx + c
where a, b, and c are real numbers and a ≠ 0.
The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value
So the maximum is if a <0 and the minimum if a> 0.
The formula for finding the coordinates of the maximum and minimum points of the quadratic function is the same.
The maximum / minimum point of the quadratic function is
[tex]\rm -\dfrac{b}{2a},-\dfrac{D}{4a}[/tex]
Where
D = b²-4ac
h height of the ball is given by the function h (t) = 92t-16t².
so the value of a <0, then it has a maximum value
Because we are looking for maximum height, then we find the value of the y coordinate, with the formula
[tex]\rm -\dfrac{D}{4a}[/tex]
h (t) = 92t-16t²
a = -16 b = 92 c = 0
D = b²-4ac
D = 92²-4.-16.0
D = 8464
Value of y = maximum height (h):
[tex]\rm h=-\dfrac{D}{4a}\\\\h=-\dfrac{8464}{4\times -16}\\\\h=\boxed{132.25\:ft}}[/tex]
Learn more
domain of the function
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the inverse of the ƒunction
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F (x) = x2 + 1 g (x) = 5 - x
htps: //brainly.com/question/2723982
