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=

Shift down by 3 units: To shift the parabola y = x^2 down by 3 units, we subtract 3 from the y-value. This gives us the equation y = x^2 - 3.Shift left by 2 units: To shift the parabola to the left by 2 units, we replace x with (x + 2) in the equation. This gives us the equation y = (x + 2)^2 - 3.Expand and simplify: Now we expand the equation y = (x + 2)^2 - 3 to check for any simplification. Expanding (x + 2)^2 gives x^2 + 4x + 4. So the equation becomes y = x^2 + 4x + 4 - 3.Final equation: Simplify the equation by combining like terms. The constant terms 4 and -3 combine to give 1. So the final equation of the new parabola is y = x^2 + 4x + 1.

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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=

The parabola $y=x^{2}$ is shifted down by $3$ units and to the left by $2$ units. $\newline$ What is the equation of the new parabola? $\newline$ $y=$

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Q. The parabola

y=x^{2}

is shifted down by

3

units and to the left by

2

units.

\newline

What is the equation of the new parabola?

\newline

y=

Shift down by $3$ units: To shift the parabola $y = x^2$ down by $3$ units, we subtract $3$ from the $y$ -value. This gives us the equation $y = x^2 - 3$ .
Shift left by $2$ units: To shift the parabola to the left by $2$ units, we replace $x$ with $(x + 2)$ in the equation. This gives us the equation $y = (x + 2)^2 - 3$ .
Expand and simplify: Now we expand the equation $y = (x + 2)^2 - 3$ to check for any simplification. Expanding $(x + 2)^2$ gives $x^2 + 4x + 4$ . So the equation becomes $y = x^2 + 4x + 4 - 3$ .
Final equation: Simplify the equation by combining like terms. The constant terms $4$ and $-3$ combine to give $1$ . So the final equation of the new parabola is $y = x^2 + 4x + 1$ .