Question

which graph represents the equation y² = -4x?

Explanation:

Step1: Identify the form of the parabola

The equation $y^{2}=-4x$ is of the form $y^{2} = 4px$, where $4p=-4$, so $p = - 1$.

Step2: Determine the properties

For a parabola of the form $y^{2}=4px$, the vertex is at the origin $(0,0)$, the focus is at $(p,0)$ which is $(-1,0)$ and the directrix is the line $x=-p$, so the directrix is $x = 1$. The parabola opens to the left since $p<0$.

Answer:

The graph with vertex at the origin $(0,0)$, focus at $(-1,0)$ and directrix $x = 1$ and opening to the left.