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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.

Which is a zero of the quadratic function f(x) = 16x^2 + 32x - 9?

Discover how to find the zeros of the quadratic function f(x) = 16x^2 + 32x - 9 using the quadratic formula. This problem involves core algebraic concepts and is ideal for students in Grades 9-11.

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