Convert the following general form to standard form of a parabola. Show your solution. 2y^2-x-12y+18=0

Answer 1

2y²- x - 12y + 18 = 0

(y - k)² - 12y = x - 18

2y²- 12y + x - 18

Complete the square

ax² - bx + c, a = 2, b = -12, c = 0 = x - 18

d = b/ 2a

d = -12/ 2•2 = -12/4 = -3

e = c - b² /4a

e = 0 - (-12)² / 4 ^• 2 = -144/8 = -18

Substitute d & e into vertex form

2(y - 3)² - 18 = x - 18

2(y - 3)² = x

(y - 3)² = x/ 2 or (y - 3)² = 1/2 x

Answer 2

2y^2 - x - 12y + 18 = 0

x = 2y^2 - 12 y + 18

x = 2(y^2 - 6y + 9)

x = 2(y-3)^2