Question 978387
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The vertical intercept is the height of the projectile at time 0.  The horizontal intercepts are at the times when the projectile is at height zero, that is, on the ground.  One of these times is negative, referring to where the ball was some time before it was thrown into the air in the first place -- in other words, an absurdity.  The positive root is the time it hits the ground.


Substitute zero for t to find the height value at time zero.  Then set the quadratic equal to zero and solve for the positive root.  Use the formula for the vertex of a parabola to find the coordinates of the vertex.  This function has a negative lead coefficient, so remember what that means in terms of the function value at the vertex.


Just like finding the time when the height will be zero, set the function equal to 1500 and solve.  Two positive roots, one on the way up, one on the way back down.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \