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What is the axis of symmetry of the parabola $x = \frac{1}{2}(y + 3)^2 + 5$ ?

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Find the axis of symmetry of a parabola

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Q. What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

?

Equation of the parabola: We have the equation of the parabola: $\newline$ $x = \frac{1}{2}(y + 3)^2 + 5$ $\newline$ This is a horizontal parabola because the variable $y$ is squared and $x$ is isolated on one side of the equation.
General form of a horizontal parabola: The general form of a horizontal parabola is $x = a(y - k)^2 + h$ , where $(h, k)$ is the vertex of the parabola. $\newline$ By comparing the given equation $x = \frac{1}{2}(y + 3)^2 + 5$ with the general form, we can identify the vertex $(h, k)$ .
Identifying the vertex: From the equation $x = \frac{1}{2}(y + 3)^2 + 5$ , we can see that the vertex $(h, k)$ is $(5, -3)$ . $\newline$ This means $h = 5$ and $k = -3$ .
Axis of symmetry: The axis of symmetry for a horizontal parabola is a vertical line that passes through the vertex. Therefore, it has the equation $y = k$ . $\newline$ Substituting the value of $k$ , we get the axis of symmetry as $y = -3$ .

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