Question

How do you write `3X=4-3X^2` in vertex form?

Answer 1

`3(x+1/2)^2-19/4`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`
where ( h , k ) are the coordinates of the vertex and a is a constant.

`"the equation of a parabola in standard form " ax^2+bx+c`

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

`"rearrange " 3x=4-3x^2" into this form"`

`rArr3x^2+3x-4rArry=3x^2+3x-4`

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

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

`"substitute this value into the standard form for y"`

`rArry_(color(red)"vertex")=3(-1/2)^2+3(1/2)-4=-19/4`

`rArrcolor(magenta)"vertex "=(-1/2,-19/4)`

`rArry=3(x+1/2)^2-19/4larrcolor(red)" in vertex form"`