Question

a parabola has a vertex at (0,0). the equation for the directrix of the parabola is x = -4. in which direction does the parabola open? up down right left

Explanation:

A parabola's vertex is midway between the focus and the directrix. The directrix here is \( x = - 4 \) (a vertical line), and the vertex is at \( (0,0) \). For a parabola, if the directrix is a vertical line (\( x=\) constant), the parabola opens horizontally (left or right). The vertex \( (0,0) \) is to the right of the directrix \( x=-4 \). A parabola opens away from the directrix. Since the directrix is at \( x = - 4 \) (left of the vertex), the parabola opens to the right (away from the directrix towards the positive \( x \)-direction).

Answer:

C. right