What is an equation of a parabola with the given vertex and focus?
vertex: (–2,5); focus: (–2, 6)
Since the vertex is (-2, 5), the equation of the parabola will have the form:
(x + 2)^2 = 4p(y - 5)
where p is the distance from the vertex to the focus (since the parabola is vertical).
Using the distance formula, we can calculate p:
p = sqrt((6 - 5)^2 + (-2 - (-2))^2) = 1
Now we can plug in the values for p and the vertex to get the final equation:
(x + 2)^2 = 4(y - 5)
or, if you prefer standard form:
4y = (x + 2)^2 + 20.