Question 983827
{{{y = ax^2 + bx + c}}}

{{{y/a = x^2 + bx/a + c/a}}}

{{{y/a - c/a = x^2 + bx/a}}}

Complete the square:



{{{y/a - c/a  + (bx/2a)^2 = x^2 + bx/a + (b/2a)^2}}}

{{{y/a -c/a + (b^2)/4a^2 = (x+(b/2a))^2}}}

{{{0+-sqrt(y/a -c/a + (b^2)/4a^2) = x + (b/2a)}}}

{{{-b/2a +- sqrt(y/a-c/a+(b^2)/4a^2) = x}}}

Get a common denominator:

{{{x = -b/2a +- sqrt((4ay - 4ac + b^2)/4a^2)}}}

{{{x = -b/2a +- sqrt((4ay - 4ac + b^2))/sqrt(4a^2)}}}

{{{x = (-b +- sqrt(b^2 - 4ac + 4ay))/2a}}} <--- ANSWER


Notice that if we plug in y = 0, this gives our quadratic formula that we are used to.