Question

A relation contains the points (negative2, 4), (negative1,1), (0,0), (1,1), and (2,4). Which statement accurately describes this relation?

Answer 1

Answer:

We have the points:

(-2,4), (-1, 1), (0, 0), (1, 1), (2, 4)

First, we can see a symmetry around the point (0, 0), then this is an even function. Where an even function is a function f(x) such that:

f(x) = f(-x)

And in this case we have:

f(-2) = 4 = f(2)

f(-1) = 1 = f(1)

Now, we can also assume that this is a quadratic function (or it behaves like a quadratic function near the range [-2, 2]).

Such that:

f(x) = a*x^2 + b*x + c

Now let's use the known points to find our equation, we start with (0, 0)

f(0) = 0 = a*0^2 + b*0 + c

then c = 0.

f(x) = a*x^2 + b*x

Now let's use the points (1, 1) and (-1, 1)

f(1) = a*1^2 + b*1 = 1 = a*(-1)^2 + b*-1

       a + b = a - b

           +b = -b

           2*b = 0

Then we must have b = 0

f(x) = a*x^2

And now we can use the point (2, 4)

f(2) = 4 = a*2^2 = a*4

Then  a = 1.

Our function is f(x) = 1*x^2