https://file.aiquickdraw.com/mathbot/file/172749161740242r8uvzp.jpg

Let's solve the quadratic function \( f(x) = x^2 + 6x + 6 \) using the quadratic formula to find the x-intercepts.

The quadratic formula is:

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

For the equation \( f(x) = x^2 + 6x + 6 \), we have:

- \( a = 1 \)
- \( b = 6 \)
- \( c = 6 \)

Now, let's substitute these values into the quadratic formula.

### Step 1: Compute the discriminant
\[
b^2 - 4ac = 6^2 - 4(1)(6) = 36 - 24 = 12
\]

### Step 2: Apply the quadratic formula
\[
x = \frac{-6 \pm \sqrt{12}}{2(1)} = \frac{-6 \pm 2\sqrt{3}}{2}
\]
Simplify:
\[
x = -3 \pm \sqrt{3}
\]

### Solution:
The zeros of the function are \( x = -3 + \sqrt{3} \) and \( x = -3 - \sqrt{3} \).

Thus, the zeros and x-intercepts are the same, and the correct choice is **B.**

Would you like a more detailed explanation of any part of this solution?

Here are 5 related questions you might find interesting:
1. How does the discriminant affect the number of real solutions in a quadratic equation?
2. What does it mean if the discriminant is negative in a quadratic equation?
3. How would the solution change if the quadratic had a higher degree, say cubic?
4. Can you solve a quadratic equation without using the quadratic formula?
5. How can completing the square be used to solve a quadratic function?

**Tip:** When solving quadratics, always check the discriminant first to quickly determine the nature of the roots!

Find the real zeros, if any, of the quadratic function f(x) = x^2 + 6x + 6 using the quadratic formula. What are the x-intercepts, if any, of the graph of the function?

Learn how to solve the quadratic function f(x) = x² + 6x + 6 using the quadratic formula to find its zeros and x-intercepts. This solution involves key algebraic concepts, such as the quadratic formula and the discriminant. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation