If a ball is thrown directly upward with a velocity of 26 ft/s, its height (in feet) after t seconds is given by y = 26t − 16t^2. What is the maximum height attained by the ball?

-Please just post answer if possible, my calculations are off. Just want to make sure I am correct.

To find the maximum height attained by the ball, we need to determine the vertex of the parabolic equation. The vertex represents the maximum or minimum point on the graph.

The equation for the height of the ball is given by y = 26t - 16t^2.

To find the vertex, we need to find the value of t that corresponds to the maximum height. The t-value of the vertex can be found using the formula t = -b / (2a), where a = -16 and b = 26.

Substituting these values into the formula, we get:
t = -26 / (2 * -16)
t = -26 / -32
t = 0.8125

To find the corresponding height, we can substitute this value back into the equation:
y = 26 * 0.8125 - 16 * (0.8125)^2

Calculating this expression:
y = 21.125

Therefore, the maximum height attained by the ball is 21.125 feet.

To find the maximum height attained by the ball, we need to determine the vertex (highest point) of the parabolic function y = 26t - 16t^2.

The vertex of a parabola is given by the formula (h, k), where h represents the x-coordinate and k represents the y-coordinate.

In our case, the equation of the parabola y = 26t - 16t^2 is already in the standard form y = ax^2 + bx + c, where a = -16, b = 26, and c = 0. This means that the x-coordinate of the vertex can be found using the formula h = -b/2a and the y-coordinate can be found by substituting the x-coordinate into the equation.

Applying this formula, we get h = -26 / (2 * -16) = 26/32 = 13/16.

To find the y-coordinate, we substitute the x-coordinate (13/16) into the function equation: y = 26*(13/16) - 16*(13/16)^2.

Evaluating this expression, we find that the maximum height attained by the ball is approximately 10.16 feet.

Therefore, the maximum height attained by the ball is approximately 10.16 feet.

well, you want y when x = -b/2a = 26/32

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