To solve the problem, we need to identify the correct quadratic function for the given parabola. Here are the steps:

Step 1: Identify the roots of the parabola

The graph shows that the parabola crosses the x-axis at $x = -1$ and $x = 3$. Therefore, the factors of the quadratic equation must be $(x + 1)$ and $(x - 3)$.

Step 2: Identify the direction of the parabola

The parabola opens downward, indicating that the coefficient of the quadratic term $x^2$ is negative. This implies a negative sign in front of the quadratic function.

Step 3: Write the equation

Based on the roots and the direction, the quadratic equation should be: $f(x) = -(x + 1)(x - 3)$

Step 4: Match with the given options

The correct answer is: $\boxed{f(x) = -(x + 1)(x - 3)}$

Would you like further explanation on any step?

Here are 5 related questions for practice:

1. How can you find the vertex of a parabola given its factored form?
2. What is the standard form of a quadratic function, and how can you convert from factored form to standard form?
3. How do you determine the axis of symmetry for a quadratic function?
4. What is the significance of the discriminant in a quadratic equation?
5. How do you find the y-intercept of a parabola from its equation?

Tip: The sign of the leading coefficient in a quadratic equation determines whether the parabola opens upward (positive) or downward (negative).