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The given equation is \( y = x^2 \), and the problem asks to find the new equation when this parabola is shifted up by 4 units.

When a parabola \( y = f(x) \) is shifted vertically, the transformation can be expressed as \( y = f(x) + k \), where \( k \) is the amount of vertical shift. In this case, the vertical shift is 4 units upwards, so we add 4 to the original equation:

\[
y = x^2 + 4
\]

Thus, the equation of the new parabola is \( y = x^2 + 4 \).

Would you like further details on how vertical shifts affect the graph, or have any other questions?

Here are five related questions you might explore:
1. How does shifting a parabola down affect its equation?
2. What is the effect of shifting the parabola \( y = x^2 \) horizontally?
3. How does changing the coefficient of \( x^2 \) affect the width of the parabola?
4. What is the vertex of the parabola \( y = x^2 + 4 \), and how is it different from \( y = x^2 \)?
5. Can you describe how the graph of \( y = x^2 + 4 \) compares to \( y = x^2 - 4 \)?

**Tip:** When graphing transformations, always remember that vertical shifts affect only the y-values while horizontal shifts affect the x-values.

The parabola y = x^2 is shifted up by 4 units. What is the equation of the new parabola?

Discover how to find the equation of a parabola y = x^2 shifted up by 4 units. This example covers vertical shifts of quadratic functions and is ideal for students in Grades 7-9.

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