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The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).

Sagot :

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)

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