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 + 228x + 110

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 + 228x + 110

Answer

Explanation:

Step1: Identify the coefficients

The quadratic - function is in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 228$, and $c = 110$.

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 $b = 228$ into the formula: $x=-\frac{228}{2\times(-16)}=\frac{228}{32}=\frac{57}{8}=7.125$.

Step3: Find the y - coordinate of the vertex

Substitute $x = 7.125$ into the equation $y=-16x^{2}+228x + 110$. $y=-16\times(7.125)^{2}+228\times7.125 + 110$. First, calculate $(7.125)^{2}=50.765625$. Then, $-16\times(7.125)^{2}=-16\times50.765625=-812.25$. $228\times7.125 = 1624.5$. $y=-812.25+1624.5 + 110$. $y=812.25+110$. $y = 922.25\approx922.3$.

Answer:

$922.3$