Question 12589
1) The axis of symmetry is given by:
{{{x = -b/2a}}}
{{{x = (-4)/2}}}
{{{x = -2}}} This is the axis of symmetry.

2)
 {{{y = x(4-x)}}}
{{{y = -x^2 + 4x}}}

The axis of symmetry:

{{{x = (-4)/-2}}}
{{{x = 2}}} This is the axis of symmetry.

3) The x-coordinate of the vertex is given by:

{{{x = -b/2a}}} The same as the axis of symmetry.

{{{x = 0/2(4)}}} The coefficient of the x-term (that's b)is 0.
{{{x = 0}}}
The y-coordinate is found by substituting x = 0 into the quadratic equation and solving for y.

{{{y = 4(0)^2 - 8}}}
{{{y = -8}}}

The vertex is at: (0, -8)

4) Factorise (UK?): {{{2x^2 - 3x - 2}}} = {{{(2x + 1)(x - 2)}}}