The graph of the equation $$h= -at^2 + bt + c$$ which describes how the height, $h$ of a hit basketball changes over time which is $t$ is shown in the figure that is below
If You alter only the $c$ term in the given equation, which gives the height at time $t = 0$, what effect the alteration has with the calculations?
A quadratic in the form of $f(x)=ax^2+bx+c$ will have $c$ as its $y$-intercept, since $f(0)=a(0)^2+b(0)+c$, and thus, $f(0)=c$.
Due to this, altering the $c$ term will change the quadratic's $y$-intercept.
The $y$ value at time $t=0$ represents the initial height of the ball.
Therefore, in your example, changing the $c$ value of the quadratic will change the initial height, or the height of the ball after $0$ seconds.