To determine which function can be used to describe the values in the table, let’s analyze the table and compare it with the given options.

Step 1: Observing the Table

The table provides pairs of $x$ and $f(x)$:

We can see that $f(x)$ is negative and decreasing rapidly. This suggests it might be a quadratic function.

Step 2: General Quadratic Form

The general quadratic form is:

$f(x) = ax^2 + bx + c$

We can test the given options (no linear terms $bx$) step by step.

Step 3: Testing $f(x) = 4x^2$

1. Substituting $x = 1$: f(1) = 4(1)^2 = 4 \quad \text{(but table shows -4)}. There is a difference of $-8$. Adjusting, we rewrite: $f(x) = 4x^2 - 8$

2. Check for $x = 2$: [ f(2) = 4(2)^2 - 8 = 4(4) - 8 = 16 - 8 = - they