Jaylen launches his new high-powered model rocket upward during the Rocket Week demonstration. The rocket flies far up into the sky before falling back down to the ground. The rocket has an initial velocity of $147\,\text{meters per second}$ . Therefore, the rocket's height above the ground in meters, $t$ seconds after being launched, can be modeled by the expression $-4.9t^2 + 147t$ . This expression can be written in factored form as $-4.9t(t - 30)$ . $\newline$ What does the number $30$ represent in the expression? $\newline$ (A)the time in seconds from when the rocket is launched until it hits the ground $\newline$ (B)the height in meters of the rocket when it is launched $\newline$ (C)the time in seconds from when the rocket is launched until it reaches the top of its flight $\newline$ (D)the height in meters of the rocket when it reaches the top of its flight

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Interpret parts of quadratic expressions: word problems

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Q. Jaylen launches his new high-powered model rocket upward during the Rocket Week demonstration. The rocket flies far up into the sky before falling back down to the ground. The rocket has an initial velocity of

147\,\text{meters per second}

. Therefore, the rocket's height above the ground in meters,

t

seconds after being launched, can be modeled by the expression

-4.9t^2 + 147t

. This expression can be written in factored form as

-4.9t(t - 30)

\newline

What does the number

30

represent in the expression?

\newline

(A)the time in seconds from when the rocket is launched until it hits the ground

\newline

(B)the height in meters of the rocket when it is launched

\newline

(C)the time in seconds from when the rocket is launched until it reaches the top of its flight

\newline

(D)the height in meters of the rocket when it reaches the top of its flight

Rocket Height Expression: The expression for the rocket's height is given in factored form as $-4.9t(t - 30)$ . $\newline$ To understand what the number $30$ represents, we need to look at the factors of the quadratic equation.
Roots of the Equation: The roots of the equation $-4.9t(t - 30) = 0$ are $t = 0$ and $t = 30$ . These roots represent the times when the height of the rocket is $0$ meters.
Rocket Launch and Landing: The first root, $t = 0$ , is the time when the rocket is launched. $\newline$ The second root, $t = 30$ , is the time when the rocket comes back down to the ground.
Highest Point Calculation: Since the rocket starts at the ground, goes up, and then comes back down, the highest point is reached at the midpoint of the time interval between the two roots.
Midpoint Time Calculation: The midpoint in time between $t = 0$ and $t = 30$ is $(0 + 30) / 2$ , which is $15$ seconds. $\newline$ This is the time when the rocket reaches the top of its flight.
Representation of Number $30$ : Therefore, the number $30$ in the expression $-4.9t(t - 30)$ represents the time in seconds from when the rocket is launched until it hits the ground.