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Answer:
The maximum height the rocket reaches is 16.
Step-by-step explanation:
You know that a model rocket is launched in the air and the quadratic function is modeled by the equation y = -16*x² + 32*x where x is measuring time and y is the height of the model rocket.
A quadratic function or function of the second degree is a polynomial function defined by:
y= a*x² + b*x + c
A quadratic function has a maximum or a minimum and the vertex formula is used to get the highest or lowest value of the function. 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").
The value of the vertex on the x-axis can be calculated with the expression [tex]x=\frac{-b}{2*a}[/tex]
The value of the vertex on the y axis must be obtained by substituting the value of the vertex on the x axis in the function y= a*x² + b*x + c
In this case, a= -16, b=32 and c=0. Since a<0 the vertex will indicate the maximum of the function.
The value of the vertex on the x-axis is [tex]x=\frac{-32}{2*(-16)}=1[/tex]
The value of the vertex on the y axis is:
y = -16*1² + 32*1
Solving:
y= -16*1 +32
y= -16 +32
y=16
The maximum height the rocket reaches is 16.