Question

How do you write `f(x) = x^2+3x-4` in vertex form?

Answer 1

`f(x)=(x+3/2)^2-25/4`

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 multiplier"`

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

`• " ensure the coefficient of the "x^2" term is 1"`

`• " add/subtract "(1/2"coefficient of x-term")^2" to "x^2+3x`

`f(x)=x^2+3x-4larr" coefficient of "x^2" term is 1"`

`color(white)(f(x))=x^2+2(3/2)xcolor(red)(+9/4)color(red)(-9/4)-4`

`color(white)(f(x))=(x+3/2)^2-25/4larrcolor(red)" in vertex form"`