How do you solve this????

Question

If Thomas jumps in the air and his position is modeled by the equation y = 3x2 - 12x, how long is Thomas in the air?

Answer 1

To determine how long Thomas is in the air, we need to find the time it takes for him to reach his maximum height, which occurs at the vertex of the parabolic path.

The x-coordinate of the vertex is given by the formula x = -b / 2a, where a and b are the coefficients of the quadratic equation. In this case, a = 3 and b = -12, so:

x = -(-12) / 2(3) = 2

Therefore, Thomas reaches his maximum height after 2 seconds.

To find his height at this time, we substitute x = 2 into the equation:

y = 3(2)2 - 12(2) = -12

So Thomas reaches a height of -12 units (presumably in feet or meters) at the peak of his jump.

However, it's worth noting that the given equation only models Thomas's vertical position and does not take into account any factors that could affect his actual time in the air, such as air resistance, gravity, or his initial velocity. So while we can determine when he reaches his maximum height, the actual duration of his jump may be different from what is predicted by the equation.