Which is a zero of the quadratic function f(x) = 16x2 + 32x − 9?

x = –5.25
x = –2.25
x = –1.25
x = –0.25

To find the zeros of the quadratic function \( f(x) = 16x^2 + 32x - 9 \), we need to solve the equation \( f(x) = 0 \).

The equation is:

\[
16x^2 + 32x - 9 = 0
\]

We can solve this quadratic equation using the quadratic formula:

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

Here, \( a = 16 \), \( b = 32 \), and \( c = -9 \). Plugging these values into the formula:

\[
x = \frac{-32 \pm \sqrt{32^2 - 4(16)(-9)}}{2(16)}
\]

\[
x = \frac{-32 \pm \sqrt{1024 + 576}}{32}
\]

\[
x = \frac{-32 \pm \sqrt{1600}}{32}
\]

\[
x = \frac{-32 \pm 40}{32}
\]

Now, solve for the two possible values of \( x \):

1. \( x_1 = \frac{-32 + 40}{32} = \frac{8}{32} = 0.25 \)
2. \( x_2 = \frac{-32 - 40}{32} = \frac{-72}{32} = -2.25 \)

The zeros of the function are \( x = 0.25 \) and \( x = -2.25 \).

Since \( x = -2.25 \) is one of the given options, it is the correct zero.

**Answer:** \( x = -2.25 \)

Would you like more details on solving quadratic equations, or do you have any questions? Here are some related questions:

1. How do you derive the quadratic formula?
2. What is the significance of the discriminant in the quadratic formula?
3. How can you factor a quadratic equation instead of using the quadratic formula?
4. What are the other methods to find the roots of a quadratic function?
5. How can graphing a quadratic function help find its zeros?

**Tip:** Always check the discriminant \( b^2 - 4ac \) to determine the nature of the roots (real and distinct, real and equal, or complex).

Learn how to find the zero of the quadratic function f(x) = 16x^2 + 32x - 9 using the quadratic formula. This problem involves solving a quadratic equation, understanding the discriminant, and applying algebraic techniques. Suitable for students in Grades 10-12.

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