The given quadratic function is $f(x) = 16x^2 + 32x - 9$.

To find the zeros of this quadratic function, we need to solve $16x^2 + 32x - 9 = 0$.

I will solve the quadratic equation using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a = 16$, $b = 32$, and $c = -9$.

Let's calculate this.The solutions to the quadratic equation $16x^2 + 32x - 9 = 0$ are:

$x_1 = 0.25 \quad \text{and} \quad x_2 = -2.25$

Since the question asks for a zero of the function from the given options, the correct answer is:

$x = -2.25$

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions for further practice:

1. How do you derive the quadratic formula?
2. What does the discriminant tell us about the nature of the roots?
3. Can a quadratic function have complex roots?
4. How do you complete the square for a quadratic function?
5. What are the vertex and axis of symmetry of the function $f(x) = 16x^2 + 32x - 9$?

Tip: When solving quadratic equations, always check the discriminant first to determine whether you have real or complex solutions.