Question

What is the axis of symmetry and vertex for the graph `y=-x^2+6x-4`?

Answer 1

`x=3,(3,5)`

Explanation:

`"given the equation of a parabola in standard form"`

`•color(white)(x)y=ax^2+bx+c color(white)(x);x!=0`

`"the x-coordinate of the vertex and axis of symmetry is"`

`x_(color(red)"vertex")=-b/(2a)`

`y=-x^2+6x-4" is in standard form"`

`"with "a=-1,b=6,c=-4`

`rArrx_(color(red)"vertex")=-6/(-2)=3`

`"substitute this value into the equation for the"`
`"corresponding y-coordinate"`

`rArry_(color(red)"vertex")=-9+18-4=5`

`rArrcolor(magenta)"vertex "=(3,5)`

`"equation of axis of symmetry is "x=3`
graph{(y+x^2-6x+4)(y-1000x+3000)=0 [-10, 10, -5, 5]}