Question

What is the vertex form of `y= 3x^2-10x-14`?

Answer 1

`y=3(x-5/3)^2-67/3`

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.

`"for a parabola in standard form " ax^2+bx+c`

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

`y=3x^2-10x-14" is in this form"`

`"with " a=3,b=-10,c=-14`

`rArrx_(color(red)"vertex")=-(-10)/6=5/3`

`"for y-coordinate, substitute this value into the equation"`

`rArry_(color(red)"vertex")=3(5/3)^2-10(5/3)-14=-67/3`

`rArrcolor(magenta)"vertex "=(5/3,-67/3)`

`rArry=3(x-5/3)^2-67/3larrcolor(red)" in vertex form"`