Question

What is the axis of symmetry and vertex for the graph `y=-3x^2-12x-3`?

Answer 1

`x=-2" and "(-2,9)`

Explanation:

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

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

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

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

`y=-3x^2-12x-3" is in standard form"`

`"with "a=-3,b=-12" and "c=-3`

`rArrx_("vertex")=-(-12)/(-6)=-2`

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

`y_("vertex")=-3(-2)^2-12(-2)-3=9`

`rArrcolor(magenta)"vertex "=(-2,9)`

`rArr"axis of symmetry is "x=-2`
graph{(y+3x^2+12x+3)(y-1000x-2000)=0 [-20, 20, -10, 10]}