Question

What is the axis of symmetry and vertex for the graph `y = 3x^2 + 4x - 9`?

Answer 1

`x=-2/3" and " (-2/3,-31/3)`

Explanation:

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

`"that is " y=ax^2+bx+c`

`"the x-coordinate of the vertex is "`

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

`"which also happens to be the equation of the axis of symmetry"`

`y=3x^2+4x-9" is in standard form"`

`"with " a=3,b=4,c=-9`

`rArrx_(color(red)"vertex")=-4/6=-2/3`

`"substitute this value into function to obtain y"`

`rArry_(color(red)"vertex")=3(-2/3)^2+4(-2/3)-9=-31/3`

`rArrcolor(magenta)"vertex "=(-2/3,-31/3)`

`"equation of axis of symmetry is " x=-2/3`