Question

The function f(t) = 4t2 − 8t + 8 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). (1 point)

Answer 1

Answer:

$f(t) = 4(t-1)^2 +4$

So then we see that the required values are:

$a = 4, h =1, k =4$

And the vertex for this case would be:

$V_x = -\frac{-8}{2*4} = 1$

$V_y = 4$

$V(1,4)$

Step-by-step explanation:

For this case we have the following function given:

$f(t) = 4t^2 -8t +8$

And we want to wrote this equation in the form a(x − h)2 + k

We can divide both sides of the equation and we got:

$\frac{f(t)}{4} = t^2 -2t +2$

Now we can comple the square in the rigth part with this:

$\frac{f(t)}{4} = t^2 -2t +1 +(2-1)$

$\frac{f(t)}{4} = (t^2 -2t +1) +(2-1)= (t-1)^2 +1$

And now we can multiply both sides by 4 and we got:

$f(t) = 4(t-1)^2 +4$

So then we see that the required values are:

$a = 4, h =1, k =4$

And the vertex for this case would be:

$V_x = -\frac{-8}{2*4} = 1$

$V_y = 4$

$V(1,4)$