Question

How do you find the axis of symmetry and the vertex for the line `y = x^2 - 6x +11`?

Answer 1

`x=3" and "(3,2)`

Explanation:

`"given the equation of a quadratic in "color(blue)"standard form"`

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

`"then the x-coordinate of the vertex which is also the"`
`"equation of the axis of symmetry is"`

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

`y=x^2-6x+11" is in standard form"`

`"with "a=1,b=-6" and "c=11`

`x_("vertex")=-(-6)/2=3`

`"substitute this value into the equation for y"`

`y_("vertex")=3^2-(6xx3)+11=2`

`color(magenta)"vertex "=(3,2)`

`"axis of symmetry is "x=3`
graph{(y-x^2+6x-11)(y-1000x+3000)=0 [-10, 10, -5, 5]}