Question

What is the vertex form of `y= x^2/10 + x/4 + 1/6`?

Answer 1

`y=1/10(x+5/4)^2+1/96`

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 multiplier"`

`"to obtain this form use "color(blue)"completing the square"`

`• " the coefficient of the "x^2" term must be 1"`

`rArry=1/10(x^2+5/2x+5/3)`

`• " add/subtract "(1/2"coefficient of x-term")^2" to"`
`x^2+5/2x`

`y=1/10(x^2+2(5/4)xcolor(red)(+25/16)color(red)(-25/16)+5/3)`

`color(white)(y)=1/10(x+5/4)^2+1/10(-25/16+5/3)`

`color(white)(y)=1/10(x+5/4)^2+1/96larrcolor(red)"in vertex form"`