Find the zeros of the function f, of, x, equals, x, squared, minus, 8, x, plus, 11, point, 7, .f(x)=x 
2
 −8x+11.7. Round values to the nearest thousandths (if necessary).

To find the zeros of the function \( f(x) = x^2 - 8x + 11.7 \), we need to solve the quadratic equation:

\[
x^2 - 8x + 11.7 = 0
\]

We can use the **quadratic formula**:

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

where \( a = 1 \), \( b = -8 \), and \( c = 11.7 \).

### Step 1: Calculate the discriminant
The discriminant is given by:

\[
\Delta = b^2 - 4ac = (-8)^2 - 4(1)(11.7)
\]

\[
\Delta = 64 - 46.8 = 17.2
\]

### Step 2: Apply the quadratic formula
Now, substitute the values into the quadratic formula:

\[
x = \frac{-(-8) \pm \sqrt{17.2}}{2(1)}
\]

\[
x = \frac{8 \pm \sqrt{17.2}}{2}
\]

\[
x = \frac{8 \pm 4.147}{2}
\]

### Step 3: Find the two solutions
Now, calculate the two possible values for \( x \):

1. \( x_1 = \frac{8 + 4.147}{2} = \frac{12.147}{2} = 6.074 \)
2. \( x_2 = \frac{8 - 4.147}{2} = \frac{3.853}{2} = 1.927 \)

### Final answer:
The zeros of the function are approximately \( x_1 = 6.074 \) and \( x_2 = 1.927 \).

Would you like further details or clarifications?

Here are 5 related questions you can explore:
1. How do you determine the nature of the roots using the discriminant?
2. What are the properties of the quadratic function based on the zeros?
3. How do the zeros relate to the graph of the quadratic function?
4. How can you complete the square to find the zeros?
5. What is the relationship between the vertex and the zeros of a quadratic function?

**Tip:** Always check the discriminant first—it tells you whether the solutions are real or complex!

Find the zeros of the function f(x) = x^2 - 8x + 11.7. Round values to the nearest thousandths (if necessary).

Learn how to find the zeros of the quadratic function f(x) = x^2 - 8x + 11.7 using the quadratic formula. This step-by-step solution demonstrates key algebraic methods, including calculating the discriminant and applying the quadratic formula. Perfect for students in Grades 9-10.

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