SOLUTION: Can someone please walk me through this. A flare is fired directly upward into the air from a boat that is experiencing engine problems. The height of the flare (in feet) abov

Question 331573: Can someone please walk me through this.
A flare is fired directly upward into the air from a boat that is experiencing engine problems. The height of the flare (in feet) above the water, t seconds after being fired, is given by the formula h = -16t2 + 96t + 12. If the flare is designed to explode when it reaches its highest point, at what height will this occur?
____feet
Thank you,
Jerry

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A flare is fired directly upward into the air from a boat that is experiencing engine problems.
The height of the flare (in feet) above the water, t seconds after being fired,
is given by the formula h = -16t^2 + 96t + 12.
If the flare is designed to explode when it reaches its highest point,
at what height will this occur?
:
h = -16t^2 + 96t + 12 is a parabola, the min/max occurs at the axis of symmetry
the coefficient of t^2 is negative so is will be a maximum
:
The formula for the axis of symmetry: x = -b/(2a)
In this equation; x=t; a=-16; b=96;
we have
t =
t =
t = +3 secs when max height will occur
:
To find the height substitute 3 sec for t in the original equation
h = -16(3^2) + 96(3) + 12
h = -16(9) + 288 + 12
h = -144 + 300
h = 156 ft is max height and occurs in 3 sec
:
:
Looks like this: h is y axis, t is x axis

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