Question

How do you identify the vertex for the graph of `y = −3x^2 + 6x − 4`?

Answer 1

`(1,-1)`

Explanation:

`"for the standard quadratic function " y=ax^2+bx+c`

`"the x-coordinate of the vertex " x_(color(red)"vertex")=-b/(2a)`

`"for " y=-3x^2+6x-4`

`a=-3,b=6" and " c=-4`

`rArrx_(color(red)"vertex")=-6/(-6)=1`

`"substitute this value into function and evaluate for y"`

`y_(color(red)"vertex")=-3(1)^2+6(1)-4=-1`

`rArrcolor(magenta)"vertex " =(1,-1)`
graph{-3x^2+6x-4 [-10, 10, -5, 5]}