Question 1206459
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Answer: <font color=red>0.5 seconds</font>


Explanation
I'll use x in place of t.


The equation we consider is
y = -16x^2+16x


Plug in y = 0 to find the x intercepts.
-16x^2+16x = 0
-16x(x - 1) = 0
-16x = 0 or x-1 = 0
x = 0 or x = 1

 
The parabola opens downward since the leading coefficient (-16) is negative.
The x intercepts are x = 0 and x = 1. 
Due to symmetry, the x coordinate of the max height occurs at the midpoint of those roots.


Add up the x intercept values and divide in half
(a+b)/2 = (0+1)/2 = 1/2 = <font color=red>0.5</font>
The max height occurs when x = <font color=red>0.5</font>
This is the final answer since your teacher wants the time value when this max height occurs.


Another way to find this value is to use the formula: h = -b/(2a) 
h = x coordinate of vertex
a,b are the first two coefficients of the function. 
In this case a = -16 and b = 16.


To find the max height itself, plug x = 0.5 into the function to find:
y = -16x^2+16x 
y = -16(0.5)^2+16(0.5) 
y = 4
The point (0.5, 4) is the highest point on the parabola.


The horse reaches the max height of 4 feet at the time 0.5 seconds.
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