Given: 2x - 5x^2 = -3y + 12
Put the equation in y = Ax^2 + By + C
Add 3y to both sides of the equation: " "2x - 5x^2 + 3y = 12
Subtract 2x from both sides: " "- 5x^2 + 3y = -2x + 12
Add 5x^2 from both sides: " "3y = 5x^2 -2x + 12
Divide both sides by 3: " "y = 5/3x^2 - 2/3x + 4
Find the y intercept by setting x = 0: " "y = 4
Find the x intercepts by setting y = 0 and using the quadratic formula:
x = (-B+- sqrt(B^2 - 4AC))/(2A)
x = (2/3 +- sqrt(4/9 - 4/1 * (5/3)* 4/1))/(2/1 * 5/3) = (2/3 +- sqrt(4/9 - 80/3))/(10/3)
x = (2/3 +- sqrt(-236/9))/(10/3)
No Real solutions since x is imaginary (negative square root).
