It is at: (-1, 0)
-1
Line of symmetry: x = 3
y=x2+2x+1 -b -2 2a= 2= -1 = axis of symmetry is negative one.
103
(x4 - 2x3 + 2x2 + x + 4) / (x2 + x + 1)You can work this out using long division:x2 - 3x + 4___________________________x2 + x + 1 ) x4 - 2x3 + 2x2 + x + 4x4 + x3 + x2-3x3 + x2 + x-3x3 - 3x2 - 3x4x2 + 4x + 44x2 + 4x + 40R∴ x4 - 2x3 + 2x2 + x + 4 = (x2 + x + 1)(x2 - 3x + 4)
y = x2 + 8x - 7 a = 1, b = 8, c = -7 the equation of the axis of symmetry: x = -b/2a x = -8/(2*1) = -4
-2x3 + 2x2 + 12x =(-2x) (x2 - x - 6) =(-2x) (x+2) (x-3)
(3x4 + 2x3 - x2 - x - 6)/(x2 + 1)= 3x2 + 2x - 4 + (-3x - 2)/(x2 + 1)= 3x2 + 2x - 4 - (3x + 2)/(x2 + 1)where the quotient is 3x2 + 2x - 4 and the remainder is -(3x + 2).
2x3 + 16 = 2(x3 + 8) = 2(x3 + 23) = 2(x + 2)(x2 - 2x + 22) = 2(x + 2)(x2 - 2x + 4)
If that's 2x2, the answer is (x + 2)(x2 + 4)
Take the derivative: y' = 2x + 4. Set equal to zero: 2x + 4 = 0 --> x = -2. Substitute into original and y = -3. Axis of symmetry is x = -2. Vertex is (-2,-3)
x2 × 2x = 2x3