Answer:
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.
