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Answer:
1) 2 seconds
2) 70 feet
Step-by-step explanation:
we have the formula h = -16x² + 64x + 6
where h = height of ball and x = time in seconds
for 1 , we want to find how long it will take the ball to reach its maximum height.
if we want to find how long it will take to reach its maximum height , then we want to find the x value of vertex ( vertex = peak point and in this situation represents the maximum height and time ) as x = time in this scenario.
the x value of the vertex can be calculated using the formula x = -b/2a
where a and b derive from the formula put in quadratic form ax² + bx + c
so we have -16x² + 64x + 6 , 16 takes the spot of a so a = -16 and 64 takes the spot of b so b = 64
x = -b/2a
b = -16 and a = 64
hence, x = -(64)/2(-16)
==> remove parenthesis
x = -64/2(-16)
==> multiply 2 and -16
x = -64/-32
==> divide -64 by -32
x = 2
The x value of the vertex is two meaning it will take two second for the ball to reach its maximum height.
For 2) we want to find how high the ball will be when it reaches its maximum height
In other words we want to find the y value of the vertex as y = height of ball and we want to find the height of the ball at its maximum height which is at the vertex.
to find the y value of the vertex we simply plug in the x value into the equation and evaluate
we have -16x² + 64x + 6 and the x value of the vertex is 2
so we get -16(2)² + 64(2) + 6
==> evaluate exponent
y = -16(4) + 64(2) + 6
==> multiply -16 and 4
y = -64 + 64(2) + 6
==> the -64 cancels out the x2 in 64(2)
y = 64 + 6
==> add 64 and 6
y = 70
The y value of the vertex is 70 meaning the ball was at 70 feet at its maximum height
For more validation check the attatched image
