1. The problem is to compute the values of various quadratic functions at integer points from $x = -4$ to $x = 4$. 2. Each function is of the form $f(x) = ax^2 + c$, where $a$ and $c$ vary. 3. We will calculate $f(x)$ for each $x$ and each given function. 4. Calculate for $f(x) = x^2$: $$f(-4) = (-4)^2 = 16$$ $$f(-3) = 9, f(-2) = 4, f(-1) = 1, f(0) = 0, f(1) = 1, f(2) = 4, f(3) = 9, f(4) = 16$$ 5. For $f(x) = -x^2$: $$f(-4) = -16$$ Similarly: $-9, -4, -1, 0, -1, -4, -9, -16$ 6. For $f(x) = -2x^2$: $$f(-4) = -2 imes 16 = -32$$ Similarly: $-18, -8, -2, 0, -2, -8, -18, -32$ 7. For $f(x) = 2x^2$: $$f(-4) = 2 imes 16 = 32$$ Similarly: $18, 8, 2, 0, 2, 8, 18, 32$ 8. For $f(x) = 3x^2$: $$f(-4) = 3 imes 16 = 48$$ Similarly: $27, 12, 3, 0, 3, 12, 27, 48$ 9. For $f(x) = -3x^2$: $$f(-4) = -48$$ Similarly: $-27, -12, -3, 0, -3, -12, -27, -48$ 10. For $f(x) = x^2 + 1$: Calculate $x^2$ then add 1: $$f(-4) = 16 + 1 = 17$$ Similarly: $10, 5, 2, 1, 2, 5, 10, 17$ 11. For $f(x) = x^2 - 1$: Calculate $x^2$ then subtract 1: $$f(-4) = 16 - 1 = 15$$ Similarly: $8, 3, 0, -1, 0, 3, 8, 15$ This completes computation of all $y$ values for the table. Final values can be used to fill the table for each function at each $x$.