the height, in meters, above the ground of a projectile is modeled by the function $f(t)=-4.9t^{2}+19.6t +…

the height, in meters, above the ground of a projectile is modeled by the function $f(t)=-4.9t^{2}+19.6t + 50$, where $t$ is the number of seconds since the object was launched.\nhow long after launch does the projectile reach its maximum height?\na. 1 second\nb. 2 seconds\nc. 4 seconds\nd. 19.6 seconds\ne. 50 seconds

the height, in meters, above the ground of a projectile is modeled by the function $f(t)=-4.9t^{2}+19.6t + 50$, where $t$ is the number of seconds since the object was launched.\nhow long after launch does the projectile reach its maximum height?\na. 1 second\nb. 2 seconds\nc. 4 seconds\nd. 19.6 seconds\ne. 50 seconds

Answer

Answer:

B. 2 seconds

Explanation:

Step1: Identify the quadratic - function form

The function $f(t)=-4.9t^{2}+19.6t + 50$ is in the form $y = ax^{2}+bx + c$, where $a=-4.9$, $b = 19.6$, and $c = 50$.

Step2: Use the formula for the vertex of a quadratic function

The $t$ - value 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 $b$

Substitute $a=-4.9$ and $b = 19.6$ into the formula $t=-\frac{b}{2a}$. $t=-\frac{19.6}{2\times(-4.9)}=\frac{19.6}{9.8}=2$ seconds.