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The parabola \( y=x^{2} \) is shifted up by 4 units. What is the equation of the new parabola? \( y=\square \)

Ask by Weston Cole. in the United States
Feb 22,2025

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Answer

The new equation is \( y = x^{2} + 4 \).

Solution

To shift the parabola y = x² upward by 4 units, you add 4 to the equation. The new equation is: y = x² + 4.

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The equation of the new parabola is \( y = x^{2} + 4 \). By shifting the original parabola \( y = x^{2} \) up by 4 units, you simply add 4 to the entire function, resulting in the vertex of the parabola now being at the point (0, 4) instead of (0, 0). Now your parabola opens upward, just like before, but all the points on the graph are raised, giving it a fresh new look while still maintaining its classic parabolic shape!

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