SOLUTION: Need help solving this quadratic equation. Please include steps on how to solve. Thank you. Imagine standing on the roof of a 1450-foot Tower. When you throw a baseball upward fr

Question 978387: Need help solving this quadratic equation. Please include steps on how to solve. Thank you.
Imagine standing on the roof of a 1450-foot Tower. When you throw a baseball upward from the roof of the tower, the ball�s height above the ground, H (in feet), can be described as a function of the time, t (in seconds), since the ball was dropped. This height function is defined by
H(t) = -16t2 + 80t +1450
Identify the vertical intercept and what does it mean in the context of the problem
After the baseball is thrown, how long will it take till the ball hits the ground?

Your answer to question #2 identifies one horizontal intercept of the equation. Identify another horizontal intercept and discuss whether it makes sense in the context of the problem.
Find the vertex of the equation and interpret its meaning in the context of the problem.
At what time(s) is the ball 1500 feet above the ground?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

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

My calculator said it, I believe it, that settles it

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