I have 4 point and I need a quadratic function that best describes them. (7, .95) (11.4, .57) (15.1, .42) (22.8, .24)

To find the quadratic function that best fits the four points \((7, 0.95)\), \((11.4, 0.57)\), \((15.1, 0.42)\), and \((22.8, 0.24)\), we will determine a quadratic equation of the form:

\[
f(x) = ax^2 + bx + c
\]

We need to solve for \(a\), \(b\), and \(c\) by setting up a system of equations using the given points.

Let me calculate the values of \(a\), \(b\), and \(c\) using these points.The quadratic function that best fits the points \((7, 0.95)\), \((11.4, 0.57)\), \((15.1, 0.42)\), and \((22.8, 0.24)\) is:

\[
f(x) = 0.00298x^2 - 0.13281x + 1.72478
\]

This is the quadratic model that describes the relationship between the given points.

Would you like further details on the process, or have any questions? Here are some related questions to explore:

1. How is least squares fitting used to find the best curve?
2. What are the applications of quadratic models in real-world data?
3. Can a quadratic model always be used for any set of four points?
4. What other types of functions (e.g., cubic, exponential) could fit these points?
5. How can we check the accuracy of this fit?

**Tip:** Quadratic functions can model data with one peak (maximum or minimum), making them useful in applications like projectile motion and optimization problems.

I have 4 points and I need a quadratic function that best describes them. (7, .95) (11.4, .57) (15.1, .42) (22.8, .24)

Discover how to find the best-fitting quadratic function for the points (7, .95), (11.4, .57), (15.1, .42), and (22.8, .24) using the least squares method. This problem involves solving for a, b, and c in the quadratic function f(x) = ax^2 + bx + c, perfect for students in Grades 10-12 studying curve fitting and algebra.

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