Question 1205580
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I'll use x in place of t.


The equation
y=-4.9t^2+51t+1.3
becomes
y=-4.9x^2+51x+1.3


You have a few options when it comes to determining the value of x that leads to the max height. This special x value is the axis of symmetry.<ul><li>Use the formula x = -b/(2a) to determine the axis of symmetry (recommended)</li><li>Completing the square. Perhaps not recommended since it takes a while and could be error-prone.</li><li>Use the quadratic formula to find the two roots and then apply the midpoint. As the name "axis of symmetry" implies, it's at the midpoint of the roots. This method may be error-prone so it's probably not recommended compared to the 1st option.</li><li>Use graphing technology such as: GeoGebra, Desmos, TI84, etc. Make sure you use x instead of t. Desmos is perhaps the most easiest to work with since you can click on the max point to display its coordinates.</li></ul>After determining the value of x (or t), plug it into the given equation to find y.
You should find that the max occurs at the approximate location (5.2040817063, 134.0040816327)


When rounding to say 3 decimal places, that would be (5.204, 134.004) 


Therefore, the max height is roughly 134.004 feet.
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