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 out the time at which the rocket will reach its max, to the nearest 100th of a second. y=-16x² + 143x + 122

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 + 143x + 122

Answer

Explanation:

Step1: Identify the function type

The given function $y = - 16t^{2}+145t + 122$ is a quadratic function of the form $y = ax^{2}+bx + c$ where $a=-16$, $b = 145$, $c = 122$.

Step2: Recall the formula for the vertex of a quadratic - function

The $t$ - value (time in this case) of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $t=-\frac{b}{2a}$.

Step3: Substitute the values of $a$ and $b$ into the formula

Substitute $a=-16$ and $b = 145$ into $t =-\frac{b}{2a}$. [ \begin{align*} t&=-\frac{145}{2\times(-16)}\ &=\frac{145}{32}\ &\approx4.53 \end{align*} ]

Answer:

$t\approx4.53$ seconds