Question

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

Answer 1

The vertex form of equation is `y=-4(x+1/2)^2+2`

Explanation:

`y=-4x^2-4x+1` or

`y=-4(x^2+x)+1` or

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

`y=-4(x+1/2)^2+2` . Comparing with vertex form of

equation `f(x) = a(x-h)^2+k ; (h,k)` being vertex we find

here `h=-1/2 , k=2 :.` Vertex is at `(-0.5,2)`

The vertex form of equation is `y=-4(x+1/2)^2+2`

graph{-4x^2-4x+1 [-10, 10, -5, 5]}

Answer 2

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

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"`

`"using the method of "color(blue)"completing the square"`

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

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

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

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

`color(white)(rArry)=-4(x+1/2)^2-4(-1/4-1/4)`

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