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

question 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 + 235x + 67

question 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 + 235x + 67

Answer

Explanation:

Step1: Identify the coefficients

The quadratic - function is (y = ax^{2}+bx + c), where (a=-16), (b = 235), (c = 67).

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 = 235) into the formula: (x=-\frac{235}{2\times(-16)}=\frac{235}{32}=7.34375).

Step3: Find the y - coordinate of the vertex

Substitute (x = 7.34375) into the equation (y=-16x^{2}+235x + 67). [ \begin{align*} y&=-16\times(7.34375)^{2}+235\times7.34375 + 67\ &=-16\times53.93046875+1725.78125+67\ &=-862.8875+1725.78125+67\ &=929.89375 \end{align*} ] Rounding to the nearest tenth, (y\approx929.9).

Answer:

929.9