Question

determine the vertex and the direction in which the following parabola opens.

$y^{2}=-4x$

enter the vertex as a point $(a,b)$.

the vertex is

check answer

Explanation:

Step1: Recall the standard - form of a parabola

The standard form of a parabola of the form $y^{2}=4px$ has its vertex at the origin $(0,0)$. The given equation is $y^{2}=-4x$, which is of the form $y^{2}=4px$ where $4p=-4$, so $p = - 1$.

Step2: Determine the vertex

For a parabola of the form $y^{2}=4px$, the vertex is always at the point $(0,0)$.

Step3: Determine the direction of opening

If $p>0$, the parabola $y^{2}=4px$ opens to the right. If $p < 0$, the parabola $y^{2}=4px$ opens to the left. Since $p=-1<0$, the parabola $y^{2}=-4x$ opens to the left.

Answer:

The vertex is $(0,0)$ and the parabola opens to the left.