@Batterydude6000, I can tell you are taking an AoPS class, so I won't be sharing the answers but I'll give hints.
1 - We transform the equation into x=y2−8y+13. We can then complete the square in y, which turns the equation into x=(y−4)2−3. See if you can solve yourself from here.
2 - Again, we can complete the square to get y=−2(x2−4x)−15. This simplifies to y=−2(x−2)2−7. Try solving it from here.
3 - To complete the square, we can add 6y and subtract 2x, then add 1 to complete the square for x and add 9 to complete the square for y. It should be pretty simple from here.
4 - Since the axis of symmetry is x=4, we can substitute that into y=a(x−h)2+k.
5 - The simplified equation of y=a(x−h)2+k is y=a(x+3)2−2. We can also tell that the parabola passes through the point (−1,0), so x=−1, y=0. Try substituting that in the equation and sees where that gets you.
Hope that helped. 
AnxiousLlama
+26396 
