We need to find the vertex of the parabola
Vertex (h,k) is given by the following formula:
[tex]\begin{gathered} (h,k) \\ h=-\frac{b}{2a} \\ k=f(h) \end{gathered}[/tex]Where, a and b are coefficients of the quadratic equation
[tex]f(x)=ax^2+bx+c[/tex]in this example:
[tex]f(x)=-0.6x^2+2.7x+6[/tex]Therefore,
a = 0.6
b = 2.7
Now, we know that, we can find vertex (h,k)
[tex]h=-\frac{2.7}{2\cdot(-0.6)}=2.25[/tex]now, let's determine k
[tex]\begin{gathered} k=f(h)=f(2.25)=-0.6\cdot(2.25)^2+2.7\cdot(2.25)+6 \\ k=9.0375 \end{gathered}[/tex]So, the vertex of the parabola is the point (2.25 , 9.0375)
This means that the maximum height of the ball is k = 9.0375 ft and it occurs h = 2.25 ft from where it was thrown
