A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out
the time at which the rocket will reach its max, to the nearest 100th of a second.
y = -16x2 + 174x + 78

6.81 seconds

Step-by-step explanation:

Equations in the form y = ax2 + bx + c  always graph as a u-shaped curve, or parabola, and its turning point is called the vertex.  For the rocket in this problem, its path will follow an upside-down u-shaped curve, so to find the time for it to get to the max height, we need to find the x-coordinate of the vertex.  Thankfully, there is a handy formula that can be used to find the x-coordinate of the vertex.  The formula is:  x = -b/2a.    

The "a" value in the formula is the coefficient of the x2 term and  the "b" value is the coefficient of the x term.   So for your equation, a = -16 and b = 218.  Inserting these into the formula, we have x = -218/(2)(-16), or x = -218/-32, so x = 6.8125.  Rounding this to the nearest 100th, we have x = 6.81 seconds, the time it will take for the rocket to reach its maximum height.

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step-by-step explanation:

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