So let's say I have a parabolic function that describes the displacement of some projectile without air resistance. Let's say it's
$$y=-4.9x^2+V_0x.$$
I want to know at what angle the projectile was fired. I notice that
$$\tan \theta_0=f'(x_0)$$ so the angle should be
$$\theta_0 = \arctan(f'(0)).$$ or
$$\theta_0 = \arctan(V_0).$$
Is this correct? I can't work out why it wouldn't be, but it doesn't look right when I plot curves.