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Given the points graphed in the following figure, use quadratic regression to find the quadratic function of best fit. Round the coefficients to three decimal places, if necessary.

To solve this problem, we'll first need to identify the coordinates of the points plotted on the graph. Then, we'll apply quadratic regression to find the quadratic function that best fits these points.

### Step 1: Identify the Coordinates
From the image, it looks like the points are approximately located at:
- Point 1: \((0, -5)\)
- Point 2: \((5, -2)\)
- Point 3: \((-5, -2)\)

### Step 2: Set Up the Quadratic Regression
A quadratic function is generally of the form:
\[
y = ax^2 + bx + c
\]
We can use these points to set up the system of equations for quadratic regression.

### Step 3: Solve the Quadratic Regression
We'll use the method of least squares or a calculator/software to find the coefficients \(a\), \(b\), and \(c\).

Let's calculate this.The quadratic function of best fit for the given points is:

\[
y = 0.12x^2 - 5
\]

This equation was obtained through quadratic regression, rounding the coefficients to three decimal places.

Would you like more details on the process, or do you have any other questions?

### Related Questions
1. What is the general formula for quadratic regression?
2. How can you verify the accuracy of a quadratic regression model?
3. How do changes in data points affect the shape of the quadratic curve?
4. What methods can be used to find the coefficients of a quadratic function?
5. How does quadratic regression differ from linear regression?

**Tip:** When graphing points and finding a best-fit curve, always ensure that you correctly identify the coordinates to minimize errors in your regression analysis.

Learn how to find the quadratic function of best fit using quadratic regression with a step-by-step solution. This problem involves identifying coordinates from a graph and applying quadratic regression to determine coefficients rounded to three decimal places.

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