https://file.aiquickdraw.com/mathbot/file/1725736151857hek9px9q.jpg

The equation provided is:

\[
y = 3x^2 - 3x + 7
\]

This equation is a quadratic equation in terms of \( x \), meaning \( y \) is expressed as a function of \( x \). For an equation to define \( y \) as a function of \( x \), each value of \( x \) must correspond to exactly one value of \( y \). 

In this case, since it is a quadratic function (a parabola), for every input \( x \), there is exactly one output \( y \). Therefore, **the equation does define \( y \) as a function of \( x \)**.

Answer: **Yes**

Would you like further details on why this is a function, or any other explanation?

Here are 5 related questions to consider:
1. How can you determine if an equation is a function by looking at its graph?
2. What is the general form of a quadratic function?
3. Can a vertical line test be used to confirm if an equation is a function?
4. How do the coefficients in a quadratic equation affect the shape of its graph?
5. Are all polynomial equations functions?

**Tip:** A quadratic equation always represents a function because it passes the vertical line test, meaning each input (x) has one unique output (y).

Determine whether the equation defines y as a function of x. y = 3x^2 - 3x + 7

This problem helps students determine if the quadratic equation y = 3x^2 - 3x + 7 defines y as a function of x. Learn how the quadratic equation and the vertical line test can be used to verify that each x-value has one corresponding y-value. Suitable for students in Grades 8-10.

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