https://file.aiquickdraw.com/mathbot/file/1730618243595nlxod6oq.jpg

To find the real zeros of the quadratic function \( f(x) = 9x^2 + 24x + 16 \), we need to solve for \( x \) when \( f(x) = 0 \). 

So, we set up the equation:
\[
9x^2 + 24x + 16 = 0
\]

### Step 1: Use the Quadratic Formula
The quadratic formula is:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \( a = 9 \), \( b = 24 \), and \( c = 16 \).

### Step 2: Substitute values into the formula
1. Calculate the discriminant \( b^2 - 4ac \):
   \[
   b^2 - 4ac = 24^2 - 4 \cdot 9 \cdot 16 = 576 - 576 = 0
   \]

Since the discriminant is \( 0 \), there is exactly one real root.

2. Substitute into the formula:
   \[
   x = \frac{-24 \pm \sqrt{0}}{2 \cdot 9} = \frac{-24}{18} = -\frac{4}{3} = -1.33
   \]

### Answer
The only real zero is:
\[
x = -1.33
\]

**Final Answer:**
- Enter `-1.33` in the answer box.

Would you like additional details or have any questions?

Here are some related questions to explore:
1. What happens when the discriminant is greater than zero?
2. How would you solve a quadratic equation with complex roots?
3. What is the significance of rounding in finding real zeros?
4. How does changing the coefficient \( a \) affect the position of the zeros?
5. How can you verify the zero using a graphing calculator?

**Tip:** Always check the discriminant before solving with the quadratic formula; it helps predict the number of real solutions.

Use a graphing calculator to find all the real zeros of the quadratic function f(x) = 9x^2 + 24x + 16. Round to the nearest hundredth.

Use a graphing calculator to find the real zeros of the quadratic function f(x) = 9x^2 + 24x + 16. This problem demonstrates how to apply the quadratic formula to find real roots, with detailed steps on solving and rounding the result. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation