Question

What are the vertex, focus and directrix of `y=x^2 + 3`?

Answer 1

Vertex is (0,3), focus is (0,3.25) and directrix is y=2.75

Explanation:

The vertex is at the point where the function is at its minimum (it would be the maximum if the `x^2` factor were negative). Hence the vertex is at the point (0,3).
The focus is a distance `1/(4a)` above the vertex. It is therefore the point (0,`3*1/4`).
The directrix is the horizontal line an equal distance below the vertex and is therefore the line `y = 2*3/4`