1) Vertex form of the equation of the parabola is [tex]v(t)=4(t-3)^2-64[/tex]
2)3 months after its creation the company will reach its lowest net value.
The net value of the company after t months is given as:
[tex]v(t) = 4t^2-24t-28[/tex]
The above parabolic equation can be written as
[tex]v(t)=4(t^2-6t+9)-64[/tex]........(1)
The general equation of a parabola is:
[tex]y = a(x-h)^2 +k[/tex]
where (h,k) is the vertex of the parabola.
So, (1) can be written in the vertex form as
[tex]v(t)=4(t-3)^2-64[/tex]
So, the vertex of the given parabola is (3, -64).
[tex]v'(t) = 8t - 24[/tex]
[tex]v''(t) =8[/tex]
So, from the second derivative test
t value corresponding to v'(t) =0 will give minimum value
[tex]8t-24=0[/tex]
[tex]t=3[/tex]
So, 3 months after its creation the company will reach its lowest net value.
Therefore, 1) Vertex form of the equation of the parabola is [tex]v(t)=4(t-3)^2-64[/tex]
2)3 months after its creation the company will reach its lowest net value.
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