Question

Given the directrix of y = -1 and focus of (0, 3), which is the equation of the parabola?

Answer 1

Answer:

$y=\dfrac{1}{8}x^2+1$

Step-by-step explanation:

Since the vertex is right between the vertex and the directrix, the y value of the vertex must be (3+(-1))/2=1. The x coordinate will just be the same as that of the focus, or in this case 0. This means that the vertex will be at (0,1). Since the graph opens toward the focus, it will be opening up, and since its vertex is at (0,1), it will have an equation of:

$y=\dfrac{1}{8}x^2+1$

Hope this helps!