SOLUTION: If y=ax^2+bx+c, make x the subject of the formula, i.e. express x in terms of a, b, c and y.

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Question 983827: If y=ax^2+bx+c, make x the subject of the formula, i.e. express x in terms of a, b, c and y.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+ax%5E2+%2B+bx+%2B+c
y%2Fa+=+x%5E2+%2B+bx%2Fa+%2B+c%2Fa
y%2Fa+-+c%2Fa+=+x%5E2+%2B+bx%2Fa
Complete the square:


y%2Fa+-+c%2Fa++%2B+%28bx%2F2a%29%5E2+=+x%5E2+%2B+bx%2Fa+%2B+%28b%2F2a%29%5E2
y%2Fa+-c%2Fa+%2B+%28b%5E2%29%2F4a%5E2+=+%28x%2B%28b%2F2a%29%29%5E2
0%2B-sqrt%28y%2Fa+-c%2Fa+%2B+%28b%5E2%29%2F4a%5E2%29+=+x+%2B+%28b%2F2a%29
-b%2F2a+%2B-+sqrt%28y%2Fa-c%2Fa%2B%28b%5E2%29%2F4a%5E2%29+=+x
Get a common denominator:
x+=+-b%2F2a+%2B-+sqrt%28%284ay+-+4ac+%2B+b%5E2%29%2F4a%5E2%29
x+=+-b%2F2a+%2B-+sqrt%28%284ay+-+4ac+%2B+b%5E2%29%29%2Fsqrt%284a%5E2%29
x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac+%2B+4ay%29%29%2F2a <--- ANSWER

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