https://file.aiquickdraw.com/mathbot/file/1727020111457a4xmrc9t.jpg

The image shows an equation:

\[
y = x^2 + 1 \quad \text{or equivalently} \quad y - 1 = x^2
\]

This is a quadratic relationship between \(y\) and \(x\). The equation \( y = x^2 + 1 \) is a parabola that opens upwards and is shifted 1 unit upwards compared to the basic parabola \( y = x^2 \).

Would you like to explore more about the graph, solving for \(x\), or its applications? Let me know!

Here are some related questions:

1. What is the domain and range of the equation \( y = x^2 + 1 \)?
2. How would the graph of \( y = x^2 + 1 \) compare to \( y = x^2 \)?
3. Can we solve for \( x \) in terms of \( y \)?
4. What would be the intercepts of this parabola on the axes?
5. How does the transformation \( y = x^2 + 1 \) affect the vertex?

**Tip:** When graphing quadratic equations, always look for transformations (shifts or stretches) from the base graph \( y = x^2 \).

Explore the quadratic function y = x^2 + 1, its transformations from the base parabola y = x^2, and understand its graphing details, vertex, and intercepts. Suitable for students in Grades 9-10.

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