# How do you graph the function, label the vertex, axis of symmetry, and x-intercepts.  y=-x^2+6x-4?

x of vertex: $x = \left(- \frac{b}{2} a\right) = - \frac{6}{-} 2 = 3$
y of vertex: $y = f \left(3\right) = - 9 + 18 - 4 = 5$
Vertex form: $f \left(x\right) = - {\left(x - 3\right)}^{2} + 5.$
Check by developing: $f \left(x\right) = - \left({x}^{2} - 6 x + 4\right) + 5 = - {x}^{2} + 6 x - 4.$ OK