Maximum value of a quadratic function
Given a quadratic function in the form:
[tex]f(x)=ax^2+bx+c[/tex]The maximum or minimum value of the function occurs at the vertex of the parabola that represents the function.
The x-coordinate of the parabola is given by:
[tex]x_m=-\frac{b}{2a}[/tex]If a is positive, then the function has a minimum value, if a is negative, then the function has a maximum value.
The height of a ball h after t seconds is given by:
[tex]h=-16t^2+64t[/tex]This is a quadratic function with a=-16, b=64, c=0
The time where the ball reaches its maximum height is:
[tex]t=-\frac{b}{2a}=-\frac{64}{2(-16)}=2\sec [/tex]Now we substitute this value in the function:
[tex]h=-16\cdot2^2+64\cdot2=-64+128=64ft[/tex]The maximum height of the ball is 64 ft
