SOLUTION: The height in feet for a ball thrown upward at 48 feet per second is given by s(t)= -16t^2+ 48t, where t is the time in seconds after the ball is tossed. What is the maximum heig

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Question 349018: The height in feet for a ball thrown upward at 48 feet per second is given by
s(t)= -16t^2+ 48t, where t is the time
in seconds after the ball is tossed. What is the maximum height that the ball will reach?
Found 2 solutions by nerdybill, haileytucki:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Because
s(t)= -16t^2+ 48t
is a "quadratic" -- a parabola that opens downwards
The max height will be at the vertex.
.
The "time" (t) when it reaches the max is the "axis of symmetry":
t = -b/(2a) = -48/(2*(-16)) = -48/(-32) = 1.5 seconds
.
Height, then is found by plugging the above back into:
s(t)= -16t^2+ 48t
s(1.5)= -16(1.5)^2+ 48(1.5)
s(1.5)= -16(2.25)+ 48(1.5)
s(1.5)= -36+ 48(1.5)
s(1.5)= -36+ 72
s(1.5)= 36 feet (this is what they're looking for)

Answer by haileytucki(390) About Me  (Show Source):
You can put this solution on YOUR website!
This is the equation for a parabola that opens downward. The quadratic equation ax^2+bx+c is already in standard form: where x = t, a = -16, b = 48, and c = 0.

The maximum height of the thrown object will be at the vertex (the maximumum value) (h, t) of the parabola.
The t-coordinate (equivalent to the x-coordnate) of the vertex (this is the time at which the object reaches its maximum height) is given by -(b/2a) where a = -16 and b = 48.

h=-16*((3)/(2))^(2)+48*((3)/(2))
Expand the exponent (2) to the expression.
h=-16*((3^(2))/((2)^(2)))+48*((3)/(2))
Expand the exponent (2) to the expression.
h=-16*((3^(2))/(2^(2)))+48*((3)/(2))
Squaring a number is the same as multiplying the number by itself (3*3). In this case, 3 squared is 9.
h=-16*((9)/(2^(2)))+48*((3)/(2))
Squaring a number is the same as multiplying the number by itself (2*2). In this case, 2 squared is 4.
h=-16*((9)/(4))+48*((3)/(2))
Multiply all the factors separated by a * in -16*((9)/(4))+48*((3)/(2)).
h=-16((9)/(4))+48((3)/(2))
Multiply -16 by each term inside the parentheses.
h=-36+48((3)/(2))
Multiply 48 by each term inside the parentheses.
h=-36+72
Add 72 to -36 to get 36.
h=36 feet in height