Question

which graph represents the function y² = -16x?

Explanation:

Step1: Identify the form of the conic - section

The equation $y^{2}=-16x$ is of the form $y^{2} = 4px$, which represents a parabola opening to the left. For the equation $y^{2}=4px$, comparing with $y^{2}=-16x$, we have $4p=-16$, so $p = - 4$.

Step2: Find the vertex and focus

The vertex of the parabola $y^{2}=4px$ is at the origin $(0,0)$. The focus of the parabola $y^{2}=4px$ is at the point $(p,0)$. Since $p=-4$, the focus is at $(-4,0)$.

Step3: Analyze the directrix

The directrix of the parabola $y^{2}=4px$ is given by the equation $x=-p$. Since $p = - 4$, the directrix is $x = 4$.

Answer:

The graph with focus at $(-4,0)$ and directrix $x = 4$ (the first graph from the left) represents the function $y^{2}=-16x$.