Question

How do you write `f(x) = x^2 - 4x - 10` in vertex form?

Answer 1

`f(x)=(x-2)^2-14`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(f(x)=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 "color(blue)"complete the square"`

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

`• " add/subtract "(1/2"coefficient of the x-term")^2" to"`
`x^2-4x`

`rArrf(x)=x^2+2(-2)xcolor(red)(+4)color(red)(-4)-10`

`color(white)(rArrf(x))=(x-2)^2-14larrcolor(red)"in vertex form"`