Answer:
At time t=0.5, the stone reaches a maximum height of h= 35.
Step-by-step explanation:
A quadratic function or function of the second degree is a polynomial function defined by:
f(x)=a*x² + b*x +c
The maximums and minimums of a function are the largest (maximum) or smallest (minimum) values of a function.
The vertex of the function is a point that is part of the parabola or quadratic function that coincides with the maximum or minimum. When a> 0, the vertex of the parabola is at the bottom of it, being a minimum (that is, the parabola opens "upward"), and when a <0 the vertex is at the top , being a maximum (that is, the parable opens "downward").
h represents the value of its abscissa (value of x).
k represents the value of its ordinate (value of f (x)).
The value of h can be calculated with the formula ![h=-\frac{b}{2*a}](https://tex.z-dn.net/?f=h%3D-%5Cfrac%7Bb%7D%7B2%2Aa%7D)
The value of k must be obtained by substituting the value of h in the function f(x)=a*x² + b*x +c
In this case: a=-16, b=16 and c=32. As a <0 the vertex is at the top , being a maximum. So:
![h=-\frac{16}{2*(-16)}=0.5](https://tex.z-dn.net/?f=h%3D-%5Cfrac%7B16%7D%7B2%2A%28-16%29%7D%3D0.5)
Substituting the value of h in the function f(x)=-16*x² + 16*x +32 you get:
f(0.5)=-16*0.5² + 16*0.5 +32
f(0.5)= 35
<u><em>At time t=0.5, the stone reaches a maximum height of h= 35.</em></u>
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