The equation shown is:

$y = x^2 - x - 12$

To find the zeros of the quadratic function (i.e., the values of $x$ where $y = 0$), we need to solve:

$x^2 - x - 12 = 0$

This is a standard quadratic equation, which can be solved using factoring, the quadratic formula, or completing the square. Let's factor this equation.

Factoring:

We need two numbers that multiply to $-12$ and add to $-1$. These numbers are $-4$ and $3$.

So, we can factor the quadratic as:

$(x - 4)(x + 3) = 0$

Solving for $x$:

Set each factor equal to zero:

1. $x - 4 = 0 \quad \Rightarrow \quad x = 4$
2. $x + 3 = 0 \quad \Rightarrow \quad x = -3$

Zeros:

The zeros of the quadratic function are $x = 4$ and $x = -3$.

Would you like more details on any part of this process?

Related Questions:

1. What is the quadratic formula, and how is it applied to this problem?
2. Can you explain the concept of "zeros" of a function in more detail?
3. How do you complete the square to solve a quadratic equation?
4. What are some real-world applications of quadratic functions?
5. How can you verify the solution by plugging values back into the original equation?

Tip: Always double-check your factorization by expanding the factors to make sure you get the original quadratic equation.