We are given function : [tex]M(t)=-t^2+10t[/tex], where t is the number of hours of after she takes the madicine.
We need to find, how many hours after Elizabeth takes her madicine is the amount of madicine in her blood is highest.
Note: The given function is a quadratic function and a quadratic function represents a parabolic shape.
The highest point on the parabola is the vertex of the parabola.
The x-coordinate of the vertex of the parabola would represent the number hours after Elizabeth takes her madicine is the amount of madicine in her blood is highest.
We know, x-coordinate of the vertex = [tex]\frac{-b}{2a}[/tex]
For the given quadratic function a= -1 and b=10.
Plugging values of a and b in x-coordinate of the vertex formula, we get
[tex]\frac{-10}{2(-1)}=\frac{-10}{-2}=5[/tex]
Therefore, after 5 hours Elizabeth takes her madicine is the amount of madicine in her blood is highest.
