Given: 2x - 5x^2 = -3y + 122x−5x2=−3y+12
Put the equation in y = Ax^2 + By + Cy=Ax2+By+C
Add 3y3y to both sides of the equation: " "2x - 5x^2 + 3y = 12 2x−5x2+3y=12
Subtract 2x2x from both sides: " "- 5x^2 + 3y = -2x + 12 −5x2+3y=−2x+12
Add 5x^25x2 from both sides: " "3y = 5x^2 -2x + 12 3y=5x2−2x+12
Divide both sides by 3: " "y = 5/3x^2 - 2/3x + 43: y=53x2−23x+4
Find the yy intercept by setting x = 0: " "y = 4x=0: y=4
Find the xx intercepts by setting y = 0y=0 and using the quadratic formula:
x = (-B+- sqrt(B^2 - 4AC))/(2A)x=−B±√B2−4AC2A
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=23±√49−41⋅(53)⋅4121⋅53=23±√49−803103
x = (2/3 +- sqrt(-236/9))/(10/3)x=23±√−2369103
No Real solutions since xx is imaginary (negative square root).
