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 + 161x + 69

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 + 161x + 69

Answer

Answer:

475.6

Explanation:

Step1: Identify the coefficients

The quadratic - function is (y = ax^{2}+bx + c), where (a=-16), (b = 161), (c = 69).

Step2: Find the x - value of the vertex

The x - value of the vertex of a quadratic function (y = ax^{2}+bx + c) is given by (x=-\frac{b}{2a}). Substitute (a=-16) and (b = 161) into the formula: (x=-\frac{161}{2\times(-16)}=\frac{161}{32}=5.03125).

Step3: Find the y - value of the vertex

Substitute (x = 5.03125) into the function (y=-16x^{2}+161x + 69). [ \begin{align*} y&=-16\times(5.03125)^{2}+161\times5.03125 + 69\ &=-16\times25.3134 + 809.03125+69\ &=-405.0144+809.03125 + 69\ &=473.01685\approx475.6 \end{align*} ]