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 out the time at which the rocket will reach its max, to the nearest 100th of a second. y = -16x² + 126x + 72

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 out the time at which the rocket will reach its max, to the nearest 100th of a second. y = -16x² + 126x + 72

Answer

Answer:

$3.94$

Explanation:

Step1: Identify the coefficients

The quadratic - function is $y = ax^{2}+bx + c$, where $a=-16$, $b = 126$, $c = 72$.

Step2: Use the formula for 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 $b = 126$ into the formula: $x=-\frac{126}{2\times(-16)}$.

Step3: Calculate the value of x

First, calculate the denominator: $2\times(-16)=-32$. Then, $x=\frac{126}{32}=\frac{63}{16}=3.9375\approx3.94$.