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The parabola \( y=x^{2} \) is shifted down by 3 units and to the left by 2 units. What is the equation of the new parabola? \( y=\square \overline{\mp=} \)

Ask by Santiago Bartlett. in the United States
Feb 22,2025

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The new equation of the parabola is \( y = (x + 2)^2 - 3 \).

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Bonus Knowledge

To shift the parabola \( y = x^2 \) down by 3 units, we subtract 3, resulting in \( y = x^2 - 3 \). Next, to shift it to the left by 2 units, we replace \( x \) with \( x + 2 \), giving us \( y = (x + 2)^2 - 3 \). Thus, the equation of the new parabola is \( y = (x + 2)^2 - 3 \). Expanding this out, we get \( y = x^2 + 4x + 4 - 3 \), simplifying to \( y = x^2 + 4x + 1 \).

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