Question

What is the vertex of `y= -3x^2 + 2x − 4`?

Answer 1

`vertex (1/3, -11/3)`

Explanation:

`a^2 + bx +c`

`y= -3x^2 + 2x − 4`

a = -3
b=2
c=-4

vertex is `(h, k)`

`h = (-b)/(2a)`

`k = f(h)` i.e. put what you found for h back into your function as x and solve for y.

`h = (-2)/(2*-3) = 1/3`

`k = (-3*1/3)^2 + 2*1/3 − 4 = -11/3`

`vertex (1/3, 1/3)`

Answer 2

`"vertex "=(1/3,-11/3)`

Explanation:

`"given the equation in standard form ";y=ax^2+bx+c`

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

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

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

`"with "a=-3,b=2" and "c=-4`

`rArrx_("vertex")=-2/(-6)=1/3`

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

`y=-3(1/3)^2+2/3-4`

`color(white)(y)=-1/3+2/3-12/3=-11/3`

`rArrcolor(magenta)"vertex "=(1/3,-11/3)`