In which direction does the parabola x – 2y^2 = –5 open? Choices: [[up][down][right][left]]

Identify Parabola Type: Identify whether the given parabola is vertical or horizontal. The equation x – 2y^2 = –5 has a squared y term and not a squared x term, which indicates that it is a horizontal parabola.Rewrite Equation: Rewrite the equation in a more standard form by isolating x on one side. Add 2y^2 to both sides of the equation to get x on one side. x – 2y^2 + 2y^2 = –5 + 2y^2 Simplify to get x = 2y^2 – 5.Determine Parabola Direction: Determine the direction in which the parabola opens. The coefficient of y^2 is positive (2), which means that the parabola opens in the direction of the positive x-axis. Since it is a horizontal parabola, the positive x-axis direction is to the right.

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In which direction does the parabola $x - 2y^2 = -5$ open? $\newline$ Choices: $\newline$ $\text{[A]up}$ $\newline$ $\text{[B]down}$ $\newline$ $\text{[C]right}$ $\newline$ $\text{[D]left}$

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Algebra 2

Identify the direction a parabola opens

Full solution

Q. In which direction does the parabola

x - 2y^2 = -5

open?

\newline

Choices:

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

\text{[D]left}

Identify Parabola Type: Identify whether the given parabola is vertical or horizontal. $\newline$ The equation $x - 2y^2 = -5$ has a squared $y$ term and not a squared $x$ term, which indicates that it is a horizontal parabola.
Rewrite Equation: Rewrite the equation in a more standard form by isolating $x$ on one side. $\newline$ Add $2y^2$ to both sides of the equation to get $x$ on one side. $\newline$ $x – 2y^2 + 2y^2 = –5 + 2y^2$ $\newline$ Simplify to get $x = 2y^2 – 5$ .
Determine Parabola Direction: Determine the direction in which the parabola opens. $\newline$ The coefficient of $y^2$ is positive ( $2$ ), which means that the parabola opens in the direction of the positive $x$ -axis. $\newline$ Since it is a horizontal parabola, the positive $x$ -axis direction is to the right.