Answer:
Vertex form is f(t) = 4 [tex](t-1)^{2}[/tex] +3 and vertex is (1, 3).
Step-by-step explanation:
It is given that f(t)= 4 [tex]t^{2}[/tex] -8 t+7
Let's use completing square method to rewrite it in vertex form.
Subtract both sides 7
f(t)-7 = 4 [tex]t^{2}[/tex] -8t
Factor the 4 on the right side.
f(t) -7 = 4( [tex]t^{2}[/tex] - 2 t)
Now, let's find the third term using formula [tex](\frac{b}{2} )^{2}[/tex]
Where 'b' is coefficient of 't' term here.
So, b=-2
Find third term using the formula,
[tex](\frac{-2}{2} )^{2}[/tex] which is equal to 1.
So, add 1 within the parentheses. It is same as adding 4 because we have '4' outside the ( ). So, add 4 on the left side of the equation.
So, we get
f(t) -7 +4 = 4( [tex]t^{2}[/tex] -2 t +1)
We can factor the right side as,
f(t) -3 = 4 [tex](t-1)^{2}[/tex]
Add both sides 3.
f(t) = 4[tex](t-1)^{2}[/tex] +3
This is the vertex form.
So, vertex is (1, 3)
