To score a field goal in football, a player kicks the ball up into the air with an initial upward velocity of $56$ feet per second. Therefore, the football's height above the ground in feet, $t$ seconds after it is kicked, can be modeled by the expression $-16t^2 + 56t$ . This expression can be written in factored form as $-16t(t - 3.5)$ . $\newline$ What does the number $3.5$ represent in the expression? $\newline$ Choices: $\newline$ (A)the height in feet of the football when the player kicks it $\newline$ (B)the time in seconds from when the player kicks the football until it lands on the ground $\newline$ (C)the height in feet of the football when it reaches its highest point $\newline$ (D)the time in seconds from when the player kicks the football until it reaches its highest point

Full solution

Q. To score a field goal in football, a player kicks the ball up into the air with an initial upward velocity of

56

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

t

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

-16t^2 + 56t

. This expression can be written in factored form as

-16t(t - 3.5)

\newline

What does the number

3.5

represent in the expression?

\newline

Choices:

\newline

(A)the height in feet of the football when the player kicks it

\newline

(B)the time in seconds from when the player kicks the football until it lands on the ground

\newline

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

\newline

(D)the time in seconds from when the player kicks the football until it reaches its highest point

Identify Expression: Identify the expression for the football's height: $-16t^2 + 56t$ .
Rewrite Expression: Rewrite the expression in factored form: $-16t(t - 3.5)$ .
Recognize Factored Form: Recognize that the factored form shows the roots of the quadratic equation, where the football's height is $0$ .
Understand Roots: Understand that one root is $t = 0$ , which is when the player kicks the football.
Identify Time Points: The other root is $t = 3.5$ , which is the other time when the football's height will be zero, meaning it hits the ground.
Conclude Time Duration: Conclude that $3.5$ represents the time in seconds from when the player kicks the football until it lands on the ground.