The parabola y=x^(2) is shifted up by 2 units and to the right by 3 units. What is the equation of the new parabola? y=◻

Apply Transformations: To find the equation of the new parabola, we need to apply the transformations to the original equation y = x^2. Shifting a graph up by k units adds k to the y-value of the function. Shifting a graph to the right by h units subtracts h from the x-value inside the function.Shift Up by 2: First, we shift the parabola up by 2 units. This means we add 2 to the original function f(x) = x^2. The new function after this shift is g(x) = x^2 + 2.Shift Right by 3: Next, we shift the parabola to the right by 3 units. This means we replace x with (x - 3) in the function g(x). The new function after this shift is h(x) = (x - 3)^2 + 2.Final Equation: Now we have the final equation of the new parabola after applying both transformations. The equation is h(x) = (x - 3)^2 + 2.

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The parabola y=x^(2) is shifted up by 2 units and to the right by 3 units.
What is the equation of the new parabola?
y=◻

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

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Q. The parabola

y=x^{2}

is shifted up by

2

units and to the right by

3

units.

\newline

What is the equation of the new parabola?

\newline

y=\square

Apply Transformations: To find the equation of the new parabola, we need to apply the transformations to the original equation $y = x^2$ . Shifting a graph up by $k$ units adds $k$ to the $y$ -value of the function. Shifting a graph to the right by $h$ units subtracts $h$ from the $x$ -value inside the function.
Shift Up by $2$ : First, we shift the parabola up by $2$ units. This means we add $2$ to the original function $f(x) = x^2$ . The new function after this shift is $g(x) = x^2 + 2$ .
Shift Right by $3$ : Next, we shift the parabola to the right by $3$ units. This means we replace $x$ with $(x - 3)$ in the function $g(x)$ . The new function after this shift is $h(x) = (x - 3)^2 + 2$ .
Final Equation: Now we have the final equation of the new parabola after applying both transformations. The equation is $h(x) = (x - 3)^2 + 2$ .