Question

What is the axis of symmetry and vertex for the graph `y=x^2-6x+8`?

Answer 1

`x=3" and "(3,-1)`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`"using the method of "color(blue)"completing the square"`

`• " ensure coefficient of "x^2" term is 1"`

`• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2-6x`

`y=x^2+2(-3)xcolor(red)(+9)color(red)(-9)+8`

`color(white)(y)=(x-3)^2-1larrcolor(red)" in vertex form"`

`rArr"vertex "=(h,k)=(3,-1)`

`"the axis of symmetry is vertical and passes through"`
`"the vertex with equation"`

`x=3`
graph{(y-x^2+6x-8)(y-1000x+3000)=0 [-10, 10, -5, 5]}