the function f(x)=-10(x)(x - 4) represents the approximate height of a projectile launched from the ground…

the function f(x)=-10(x)(x - 4) represents the approximate height of a projectile launched from the ground into the air as a function of time in seconds, x. how long, from launch to landing, does the projectile stay in the air?\n0 seconds\n1 second\n2 seconds\n4 seconds

the function f(x)=-10(x)(x - 4) represents the approximate height of a projectile launched from the ground into the air as a function of time in seconds, x. how long, from launch to landing, does the projectile stay in the air?\n0 seconds\n1 second\n2 seconds\n4 seconds

Answer

Explanation:

Step1: Set height to 0

The projectile is on the ground when $f(x)=0$. So we set $- 10x(x - 4)=0$.

Step2: Solve the equation

Using the zero - product property, if $ab = 0$, then either $a = 0$ or $b = 0$. Here, $a=-10x$ and $b=x - 4$. For $-10x=0$, we get $x = 0$ (this is the launch time). For $x - 4=0$, we solve for $x$ and get $x=4$ (this is the landing time).

Answer:

D. 4 seconds