Question

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

Answer 1

`y=4(x+1/8)^2+95/16`

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 express in this form use "color(blue)"completing the square"`

`y=4x^2+x+6`

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

`rArry=4(x^2+1/4x+3/2)`

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

`"to "x^2+1/4x`

`rArry=4(x^2+2(1/8)xcolor(red)(+1/64)color(red)(-1/64)+3/2)`

`color(white)(rArry)=4(x+1/8)^2+(4xx95/64)`

`color(white)(rArry)=4(x+1/8)^2+95/16`