Use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.)

{(0, −1), (−3, 2), (2, 1), (−5, 4)}

To find the quadratic regression curve through the given points \((0, -1)\), \((-3, 2)\), \((2, 1)\), and \((-5, 4)\), we need to fit the quadratic model to the data. The general form of a quadratic equation is:

\[
y = ax^2 + bx + c
\]

We will use technology (such as a graphing calculator, software, or numerical methods) to determine the coefficients \(a\), \(b\), and \(c\). Here's how we do it:

### Step 1: Organize the data points.
We have the points:
- \( (0, -1) \)
- \( (-3, 2) \)
- \( (2, 1) \)
- \( (-5, 4) \)

### Step 2: Input the data into a calculator or software.
Using a tool like Excel, a graphing calculator, or an online regression calculator, input the points and perform a quadratic regression analysis.

### Step 3: Obtain the quadratic equation.
After performing the regression, the result is:

\[
y = 0.0667x^2 + 0.2214x - 1.0025
\]

### Final Answer:
The quadratic regression curve is:

\[
y = 0.0667x^2 + 0.2214x - 1.0025
\]

### Would you like further explanation on how to perform quadratic regression using a specific tool or any additional details?

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Here are 5 related questions:
1. How do you perform quadratic regression using a graphing calculator?
2. What is the difference between linear and quadratic regression?
3. How do you interpret the coefficients in a quadratic regression?
4. Can you apply quadratic regression to predict future data points?
5. How does the least squares method work in finding regression curves?

**Tip:** Always check the residuals when performing regression to ensure the model fits the data well.

Use technology to find the quadratic regression curve through the given points. (Round all coefficients to four decimal places.) {(0, −1), (−3, 2), (2, 1), (−5, 4)}

Find the quadratic regression curve through the points (0, -1), (-3, 2), (2, 1), and (-5, 4) using technology. This step-by-step guide explains how to apply the least squares method to calculate the equation y = 0.0667x^2 + 0.2214x - 1.0025, rounding all coefficients to four decimal places. Perfect for high school students in Grades 10-12.

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