During a round of golf, a player hits the ball with an initial upward velocity of $72$ feet per second. Therefore, the ball's height above the ground in feet, $t$ seconds after it is hit, can be modeled by the expression $-16t^2 + 72t$ . This expression can be written in factored form as $-16t(t - 4.5)$ . $\newline$ What does the number $4.5$ represent in the expression? $\newline$ (A)the time in seconds from when the player hits the ball until it reaches its highest point $\newline$ (B)the time in seconds from when the player hits the ball until it lands on the ground $\newline$ (C)the height in feet of the ball when it reaches its highest point $\newline$ (D)the height in feet of the ball when the player hits it

Full solution

Q. During a round of golf, a player hits the ball with an initial upward velocity of

72

feet per second. Therefore, the ball's height above the ground in feet,

t

seconds after it is hit, can be modeled by the expression

-16t^2 + 72t

. This expression can be written in factored form as

-16t(t - 4.5)

\newline

What does the number

4.5

represent in the expression?

\newline

(A)the time in seconds from when the player hits the ball until it reaches its highest point

\newline

(B)the time in seconds from when the player hits the ball until it lands on the ground

\newline

(C)the height in feet of the ball when it reaches its highest point

\newline

(D)the height in feet of the ball when the player hits it

Expression for ball's height: The expression for the ball's height is $-16t^2 + 72t$ , which factors to $-16t(t - 4.5)$ .
Roots of quadratic equation: The factored form shows the roots of the quadratic equation, which are the values of $t$ where the height is zero (when the ball is on the ground).
Time to reach highest point: One root is $t = 0$ , which is when the player hits the ball. The other root is $t = 4.5$ , which is the other time the ball will be on the ground.
Calculation for $4.5$ seconds: Since the ball starts on the ground, goes up, and comes back down, the time it takes to reach the highest point is halfway between the two times it's on the ground.
Calculation for $4.5$ seconds: Since the ball starts on the ground, goes up, and comes back down, the time it takes to reach the highest point is halfway between the two times it's on the ground.Halfway between $0$ and $4.5$ seconds is $2.25$ seconds, but we're looking for what $4.5$ represents, not the halfway point.