Question

40 points!! What does this graph represent

Answer 1

Answer:

$f(x)=0.2\,(x-2)^2+1$

Option "B" as per the list of possible answers

Step-by-step explanation:

Notice that the parabola has a minimum at the point (2, 1), therefore first look at which of the options gives you  $f(2) = 1$. You would be able then the discard the last two functions listed (they render "-1" (not 1) for x = 2.

Now to decide between the first and the second option, notice that the first option has a negative coefficient (-0.2) multiplying the perfect square $(x-2)^2$ which means that the branches of such parabolic function would be pointing down. So you discard the first option, and now the only one left is the second option:

$f(x)=0.2\,(x-2)^2+1$

which you can check briefly by evaluating a couple of easy points  (like what values you get for x = 0, and at x = 4, and confirm it is the correct option.