Writing x squared minus 6x minus 8y minus 7 equals 0 in standard form gives which vertex and focus?

1. Only x is squared, so the axis of symmetry is parallel to the y-axis. 2. Move the other terms across to get x squared minus 6x equal to 8y plus 7. 3. Half of 6 is 3 and 3 squared is 9, so add 9 to both sides to complete the square. 4. The left side becomes (x - 3) squared and the right becomes 8y plus 16. 5. Factoring the right gives (x - 3) squared equals 8(y + 2), so the vertex is (3, -2). 6. Setting 4p equal to 8 gives p equal to 2, and since p is positive the curve opens up. 7. The focus is (h, k + p), which is (3, -2 + 2), or (3, 0). 8. The focus (3, -4) subtracts p instead of adding it, which locates the directrix. 9. The vertex (-3, 2) flips both signs when reading h and k out of the binomials. 10. The vertex (3, 2) drops the sign on k after the factoring step. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.3 The Parabola_