To find a quadratic function that models the values in the table, we will assume the general form of a quadratic function:

$y = ax^2 + bx + c$

We will use the points provided in the table to create a system of equations and solve for $a$, $b$, and $c$.

Points from the table:

1. $(-1, -3)$
2. $(0, -3)$
3. $(3, 33)$

We can substitute these points into the quadratic function:

1. For $(-1, -3)$: $-3 = a(-1)^2 + b(-1) + c \Rightarrow -3 = a - b + c$

2. For $(0, -3)$: $-3 = a(0)^2 + b(0) + c \Rightarrow -3 = c$

3. For $(3, 33)$: $33 = a(3)^2 + b(3) + c \Rightarrow 33 = 9a + 3b + c$

From equation 2, we know that $c = -3$. Now, we can substitute $c = -3$ into the other two equations:

1. $-3 = a - b - 3 \Rightarrow a - b = 0 \Rightarrow a = b$
2. $33 = 9a + 3b - 3 \Rightarrow 36 = 9a + 3b \Rightarrow 36 = 12a \Rightarrow a = 3$

Since $a = b$, we also have $b = 3$.

Thus, the quadratic function is:

$y = 3x^2 + 3x - 3$

This is the quadratic function that models the values in the table.

Would you like more details on solving this system, or do you have any other questions?

Here are 5 related questions you might find helpful:

1. How do you solve a system of equations using substitution or elimination?
2. What is the significance of each term in a quadratic function $y = ax^2 + bx + c$?
3. How can you determine the vertex of a quadratic function?
4. What is the role of the discriminant in a quadratic equation?
5. How can quadratic functions model real-world scenarios?

Tip: When modeling with quadratics, always try to use points that cover a range of values for $x$ to ensure an accurate fit.