Question 37115
{{{y = -x^2 + 4x - 3}}}
first find the roots, if any
{{{-x^2 + 4x - 3 = 0}}}
multiply both sides by -1
{{{x^2 - 4x + 3 = 0}}}
{{{(x - 3)*(x - 1) = 0}}}
***note***
the above equation with the signs reversed is ONLY for finding
the roots - it is not for anything else - the actual equation is
the one you started with
****************
the roots are +3 and +1
those are the values for x that make the above true
the axis of sym will be in the middle of the roots
{{{(r1 + r2) / 2 = a}}}
{{{(3 + 1) / 2 = +2}}}
The equation of the axis of symmety is x = 2
The vertex is on the axis of symmetry, so
find what y is when x = 2
{{{y = -(2^2) + 4(2) - 3}}}
{{{y = -4 +8 - 3}}}
{{{y = +1}}}
So, the vertex is at (2,1)
{{{ graph( 300, 300, -2, 5, -5, 2, -(x^2) +4*x -3) }}}