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In which direction does the parabola $x + y^2 = -7$ open? $\newline$ Choices: $\newline$ (A) $\text{up}$ $\newline$ (B) $\text{down}$ $\newline$ (C) $\text{right}$ $\newline$ (D) $\text{left}$

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Find properties of a parabola from equations in general form

Full solution

Q. In which direction does the parabola

x + y^2 = -7

open?

\newline

Choices:

\newline

(A)

\text{up}

\newline

(B)

\text{down}

\newline

(C)

\text{right}

\newline

(D)

\text{left}

Identify general form: Identify the general form of the parabola equation. $\newline$ The given equation is $x + y^2 = -7$ . This equation has a squared $y$ term and no squared $x$ term, indicating that it is a horizontal parabola.
Rewrite to isolate x: Rewrite the equation to isolate x. $\newline$ To find the direction of the opening, we need to express x in terms of y. We can do this by subtracting $y^2$ from both sides of the equation. $\newline$ $x = -y^2 - 7$
Determine opening direction: Determine the direction of the opening. $\newline$ The coefficient of $y^2$ is $-1$ . Since the coefficient is negative, the parabola opens in the negative $x$ -direction, which is to the left.

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