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 + 170x + 85

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 + 170x + 85

Answer

Explanation:

Step1: Identify the coefficients

The quadratic - function is (y = ax^{2}+bx + c), where (a=-16), (b = 170), (c = 85).

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}). [x=-\frac{170}{2\times(-16)}=\frac{170}{32}=\frac{85}{16}=5.3125]

Step3: Find the y - coordinate of the vertex

Substitute (x = 5.3125) into the function (y=-16x^{2}+170x + 85). [y=-16\times(5.3125)^{2}+170\times5.3125 + 85] [y=-16\times28.2265625+903.125 + 85] [y=-451.625+903.125 + 85] [y=536.5]

Answer:

536.5