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:

Step1: Recall parabola - directrix property

For a parabola with vertex \((h,k)=(0,0)\), if the directrix is a vertical line \(x = -p\), the standard - form of the parabola equation is \((y - k)^2=4p(x - h)\) when the parabola opens horizontally and \(x=h - p\) is the directrix.

Step2: Determine the value of \(p\)

Given the directrix \(x=-4\) and \(h = 0\), and the formula \(x=h - p\), we have \(0 - p=-4\), so \(p = 4\).

Step3: Determine the opening direction

Since \(p>0\) and the equation of the directrix is \(x=-4\) (a vertical line), the parabola opens to the right. The general form of a parabola with vertex \((0,0)\) and directrix \(x=-p\) is \(y^{2}=4px\) which opens to the right when \(p>0\).

Answer:

right