A ball is thrown from the top of a building. It's height (y) in feet at any given time (x) in seconds is y=-16x^2+240. What is the maximum height of the ball?
Since there is no t term in the equation the ball was "dropped" from a height of 240 ft.
So the maximum height was 240 ft
To find the maximum height of the ball, we need to determine the vertex of the parabolic function that represents the height of the ball.
The general formula for a quadratic function in the form of y = ax^2 + bx + c is y = -16x^2 + 240 in this case.
The vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula: x = -b/2a.
For the equation y = -16x^2 + 240, a = -16 and b = 0.
Plugging the values into the formula, we can find the x-coordinate of the vertex:
x = -b/2a = -0/(2*(-16)) = 0.
Therefore, the x-coordinate of the vertex is 0.
To find the y-coordinate of the vertex, substitute the x-coordinate into the original equation:
y = -16(0)^2 + 240 = 240.
Therefore, the y-coordinate of the vertex is 240.
Hence, the maximum height of the ball is 240 feet.