Question 909603
y=-x^2+5x-3  y-intercept(when x = 0) is -3
y = -(x-5/2)^2 + 25/4 - 12/4
y = -(x-5/2)^2 + 13/4
0= -(x-5/2)^2 + 13/4
x = 5/2 ± sqrt(13)/2
the vertex form of a Parabola opening up(a>0) or down(a<0), {{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry

axis of symmetry, x = 5/2
y-intercept, -3
 x-intercepts: 5/2 ± sqrt(13)/2
{{{drawing(300,300,   -6, 6, -6, 6, grid(1), blue(line(2.5,6,2.5,-6)) ,
circle(0, -3,0.2),
circle(5/2, sqrt(13)/2,0.2),
circle(2.5 + sqrt(13)/2,0,0.2),
circle(2.5 - sqrt(13)/2,0,0.2),

graph( 300, 300, -6, 6, -6, 6,0, -x^2+5x-3) )}}}