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The parabola
y=x^(2) is shifted down by 6 units and to the right by 5 units.
What is the equation of the new parabola?

y=

The parabola $y=x^{2}$ is shifted down by $6$ units and to the right by $5$ units. $\newline$ What is the equation of the new parabola? $\newline$ $y=$

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Transformations of functions

Full solution

Q. The parabola

y=x^{2}

is shifted down by

6

units and to the right by

5

units.

\newline

What is the equation of the new parabola?

\newline

y=

Shift down by $6$ units: To shift the parabola $y = x^2$ down by $6$ units, we need to subtract $6$ from the $y$ -value of the original parabola. This gives us a new equation $y = x^2 - 6$ .
Shift right by extbf{ extit{ $5$ }} units: Next, to shift the parabola to the right by extbf{ extit{ $5$ }} units, we need to replace extit{x} with extit{(x - $5$ )} in the equation. This gives us the new equation extit{y = (x - $5$ )^ $2$ - $6$ }.

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\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

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\text{}(B)g(x) = 9|x-2| - 4\text{]}

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Question

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