a rocket is launched from a tower. the height of the rocket, y in feet, is related to the time after launch…

a rocket is launched from a tower. the height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -16x² + 149x + 60

a rocket is launched from a tower. the height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -16x² + 149x + 60

Answer

Explanation:

Step1: Identify the coefficients

The quadratic - function is in the form (y = ax^{2}+bx + c), where (a=-16), (b = 149), and (c = 60).

Step2: Find the x - coordinate of the vertex

The x - coordinate of the vertex of a quadratic function (y = ax^{2}+bx + c) is given by (x=-\frac{b}{2a}). Substitute (a=-16) and (b = 149) into the formula: [x=-\frac{149}{2\times(-16)}=\frac{149}{32}=4.65625]

Step3: Find the y - coordinate of the vertex

Substitute (x = 4.65625) into the function (y=-16x^{2}+149x + 60). [y=-16\times(4.65625)^{2}+149\times4.65625 + 60] [y=-16\times21.68261719+693.78125+60] [y=-346.921875+693.78125+60] [y = 406.859375\approx406.9]

Answer:

406.9