develop a word problem question that you need to create an quadratic equation in factored from for the curve that bests fits when given a table of values in the question. The table of values needs to have 7 entries with decimals to represent a curve that best fits. instead of using x-intercepts, have only 2 y-values that are equal distance from the axis of symmetry.

Here’s a word problem that fits your request:

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**Word Problem:**

Maria is designing a parabolic fountain feature for a garden. The shape of the water stream can be modeled by a quadratic equation. She measured the height of the water stream at various points from the fountain’s center. The distances from the center are recorded as \( x \) meters, and the corresponding heights \( y \) in meters are measured.

Maria recorded the following table of values to represent the height of the stream at various points:

| Distance from the center (x) | Height of the water stream (y) |
|:----------------------------:|:-----------------------------:|
|              -3.0            |              0.8              |
|              -2.0            |              2.5              |
|              -1.0            |              3.6              |
|               0.0            |              4.0              |
|               1.0            |              3.6              |
|               2.0            |              2.5              |
|               3.0            |              0.8              |

From this data, find the quadratic equation in factored form that best fits the curve representing the water stream. Notice that two points on the curve (e.g., \(x = -2\) and \(x = 2\)) have the same height, indicating that they are equidistant from the axis of symmetry.

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This problem requires creating a quadratic equation in factored form. You can use symmetry and data points to derive the equation and express it in the form \(y = a(x - h)^2 + k\).

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Would you like me to go through solving this step-by-step?  
Here are 5 related questions to extend your learning:

1. How can we determine the axis of symmetry from the table of values?
2. How do we find the vertex of the quadratic equation from the table?
3. What is the relationship between the values of \(x = -2\) and \(x = 2\) in the equation?
4. How does changing the value of \(a\) in a quadratic equation affect the shape of the parabola?
5. How can you verify that the equation derived is the best fit for the data?

**Tip:** When solving word problems with quadratic equations, always look for symmetry in the data—it helps identify the axis of symmetry and the vertex.

Develop a word problem question that you need to create a quadratic equation in factored form for the curve that best fits when given a table of values in the question. The table of values needs to have 7 entries with decimals to represent a curve that best fits. Instead of using x-intercepts, have only 2 y-values that are equal distance from the axis of symmetry.

Solve a quadratic equation word problem involving the best fit curve from a table of values with 7 entries. Learn how to identify the axis of symmetry and equidistant points on a parabola to create the equation in factored form. Ideal for students in Grades 9-11.

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