Question

What is the axis of symmetry and vertex for the graph `g(x)=x^2-5x+2`?

Answer 1

`x=5/2" and "(5/2,-17/4)`

Explanation:

`"given quadratic in standard form "ax^2+bx+c;a!=0`

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

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

`g(x)=x^2-5x+2" is in standard form"`

`"with "a=1,b=-5" and "c=2`

`rArrx_(color(red)"vertex")=-(-5)/2=5/2`

`rArr"equation of axis of symmetry is "x=5/2`

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

`y=(5/2)^2-5(5/2)+2=-17/4`

`rArrcolor(magenta)"vertex "=(5/2,-17/4)`
graph{(y-x^2+5x-2)(y-1000x+2500)=0 [-10, 10, -5, 5]}