Question

What is the equation of a parabola if the coordinates of its vertex are (1,4) and those of its focus are (-3,4)?

Answer 1

well, let's take a peek at the parabola points


the focus is 4 points away from the vertex, that means is a really wide concave parabola, that means it has a wide "hump"

bear in mind that, from the 2 points given, the vertex and the focus, the "y" didn't change, the "x" did, that means is moving over the x-axis, or is a horizontal parabola

the focus is at the "left" of the vertex, meaning is opening to the left,
meaning the equation will look like
\(\large x=-a(y-k)^2+k\)