Answer: Option D
[tex]t_{max} =19\ s[/tex]
Step-by-step explanation:
Note that the projectile height as a function of time is given by the quadratic equation
[tex]h = -12t ^ 2 + 456t[/tex]
To find the maximum height of the projectile we must find the maximum value of the quadratic function.
By definition the maximum value of a quadratic equation of the form
[tex]at ^ 2 + bt + c[/tex] is located on the vertex of the parabola:
[tex]t_{max}= -\frac{b}{2a}[/tex]
Where [tex]a <0[/tex]
In this case the equation is: [tex]h = -12t ^ 2 + 456t[/tex]
Then
[tex]a=-12\\b=456\\c=0[/tex]
So:
[tex]t_{max} = -\frac{456}{2*(-12)}[/tex]
[tex]t_{max} =19\ s[/tex]
