+1206 The graph of the parabola \(x = 2y^2 - 6y + 3\) has an x-intercept \((a,0)\) and two y-intercepts \((0,b)\) and \((0,c)\). Find \(a + b + c\).
+128406 x = 2y^2 - 6y + 3
The x intercept is easy....let y = 0 and the x intercept is (3, 0) = (a, 0)
To find the y intercepts.....let x = 0 and solve for y
2y^2 - 6y + 3 = 0
Use the quadratic formula
y = 6 ±√[ 6^2 - 4*3 * 2 ] 6 ±√ [ 36 - 24] 6 ±√12
________________ = ______________ = __________
2 *2 4 4
The sum of these two roots = b + c = 2 (6/4) = 3
So
a + ( b + c) = 3 + (3) = 6
