How do I re-express a function in terms of "y" ?

Question

y= -x^2+x+2 I need to have this in y terms, so x= ?

Answer 1

y= -(x-.5)^2+2.25
so y-2.25=-(x-.5)^2
so (2.25-y)=(x-.5)^2
and finally, x=+-sqrt(2.25-y) +.5

Answer 2

Multiply by -1 on both sides
-y = x^2 - x - 2
x^2 - x = 2 - y
Complete the square
x^2 - x + (1/2)^2 - (1/2)^2 = 2 - y
(x - 1/2)^2 - 1/4 = 2 - y
(x - 1/2)^2 = (9/4) - y
x - 1/2 = +/- sqrt ( (9/4) - y)
x = (1/2) +/- sqrt ( (9 - 4y) / 4 )
Answer:
x = (1/2) +/- (1/2) sqrt ( 9 - 4y)

You could also use the quadratic formula instead of completing the square.

Answer 3

y = -x² + x + 2
-y = x² - x - 2
2-y = x² - x
2 - y + 1/4 = x² - x + 1/4
5/4 - y = (x - 1/2)²
±√(5/4 - y) = x - 1/2
1/2 ± √(5/4 - y) = x

Answer 4

-y= x^2-x-2 (I got rid of the negative on the x^2)
-y+2=x^2-x (complete the square)
-y+2+1/4=x^2-x+(1/4)
-y+9/4=(x-1/2)^2
+/-sqrt(-y+9/4)=x-1/2
x= +/- sqrt(-y+9/4)+1/2

Answer 5

That will not be a function.