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I'm in 8th grade and 13 years of age. My question is:

A parabola has focus (4, 0) and directrix x = -4. What is the equation of the parabola? Also, how can I use this information to tell if the parabola opens up or down (like without graphing it?)

Thank you very much for your time and volunteering!

The standard equation is (y-k)^2 = 4a(x-h) where (h,k) is the vertex. The distance from the vertex to the focus is "a" and that's also the distance from the vertex to the directrix. So in this case, the focus is at (0,0) and the equation is y^2 = 16x, opening to the right.

Algebra

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