Vertex: (4, -7); Focus: (3, -7)

Question

1. Find the standard form of the equation of the parabola using the information given.

Vertex: (4, -7); Focus: (3, -7)

Answer 1

Vertex and Focus of these points lie on a horizontal line, so that means your parabola is going to open sideways.

 

So your equation is in the form (y-k)^2 = 4p(x-h), where focus is at (h+p,k) and vertex is at (h,k)

 

If h = 4 from the vertex and h + p = 3 from the focus, p = -1 in your parabola.

 

So your equation looks like (y--7)^2 = -4(x - 4). Clean that up and you're all set.