2y^2 - x +20y = -53 Complete the square using parabola

2[y + 5]^2        =     x - 3

Step-by-step explanation:

Rewrite the given quadratic with the "x" on the right side:

2y^2 + 20y = x - 53

Now factor out '2' from the terms on the left:

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

Complete the square of (y^2 + 10y):  we get (y^2 + 10y + 25 - 25).  Then our

original 2(y^2 + 10y) = x - 53 becomes

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

2( [y + 5]^2 - 25) = x - 53, or

2[y + 5]^2 - 50    = x - 53, which reduces to

2[y + 5]^2        =     x - 3

The vertex of this parabola is at (3, -5).  The graph opens to the right (that is, the parabola is horizontal).  There is horizontal stretching by a factor of 2.