parabora

Hi white cat, you were in star bucks yesterday I seem to recall.  I like studying in coffee shops too but I didn't know that they would allow white cats in ://

There are not many Star Bucks in Australia and there are none around here so what would I know.  ://

#Write the equation of the parabola x = 2⋅y^2 −20⋅y+53 in vertex form x−h = a(y−k)^2

$x=2y^2-20y+53\\ x-53=2y^2-20y\\ x-53=2(y^2-10y)\\ \frac{x-53}{2}=y^2-10y\\ \frac{x-53}{2}+(\frac{10}{2})^2=y^2-10y+(\frac{10}{2})^2\\ \frac{x-53}{2}+25=y^2-10y+25\\ \frac{x-53}{2}+\frac{50}{2}=(y-5)^2\\ x-53+50=2(y-5)^2\\ x-3=2(y-5)^2\\ $

 x = 2⋅y^2 −20⋅y+53     subtract 53 from both sides

x - 53 =  2y^2 - 20y      factor out 2 on the right

x - 53  =   2(y^2 - 10y)   complete the square on y

x - 53   = 2 (y^2 -10y + 25   - 25 )    simplify

x - 53 = 2(y - 5)^2   - 50     add 50 to both sides

x - 3  = 2(y - 5)^2