Find the zeros of the function f, of, x, equals, minus, 1, point, 2, x, squared, plus, 6, x, minus, 5, .f(x)=−1.2x 
2
 +6x−5. Round values to the nearest thousandths (if necessary).


To find the zeros of the function \( f(x) = -1.2x^2 + 6x - 5 \), we need to solve for \(x\) when \(f(x) = 0\). This gives the quadratic equation:

\[
-1.2x^2 + 6x - 5 = 0
\]

We'll use the quadratic formula to find the solutions. The quadratic formula is:

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

For the equation \( -1.2x^2 + 6x - 5 = 0 \), the coefficients are:
- \( a = -1.2 \)
- \( b = 6 \)
- \( c = -5 \)

Now let's plug these values into the quadratic formula.

\[
x = \frac{-6 \pm \sqrt{6^2 - 4(-1.2)(-5)}}{2(-1.2)}
\]

I'll compute the solutions.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to walk through the steps manually, or would you prefer to try another method? 

Here are five questions to expand on the topic:
1. What is the importance of finding zeros of quadratic functions?
2. How can the discriminant of a quadratic equation help in determining the nature of the roots?
3. What happens if the discriminant is negative in the quadratic formula?
4. Can we apply factorization instead of the quadratic formula in this problem?
5. What role does the leading coefficient (the \( a \) term) play in the shape of the parabola?

**Tip**: When solving quadratics, always check the discriminant first—it helps predict the number and type of solutions!

Find the zeros of the function f(x) = -1.2x^2 + 6x - 5. Round values to the nearest thousandths (if necessary).

Discover how to find the zeros of the function f(x) = -1.2x^2 + 6x - 5 by applying the quadratic formula. This step-by-step guide will walk you through solving for the roots, including rounding to the nearest thousandths. Ideal for students in Grades 9-10, this problem covers key concepts in algebra and quadratic equations.

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