Question

X^2+4x-5 can be written as (x+p)^2+q. Find P and Q?

I know how to convert it into the final form but what i do not know is how to determine if the answer would be positive or negative

Answer 1

`p = 2`

`q = -9`

Explanation:

Assuming your question is stated as below :

`x^2 +4x-5` can be written as `(x+p)^2 +q`

`=> x^2+4x-5` is equal to `(x+2)^2-9`

By comparison,

`:. p = 2 and q = -9`

Answer 2

`p=2" and "q=-9`

Explanation:

`"convert to vertex form using "color(blue)"completing the square"`

`•color(white)(x)y=a(x-h)^2+klarrcolor(blue)"vertex form"`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`• " 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`

`=x^2+2(2)xcolor(red)(+4)color(red)(-4)-5`

`=(x+2)^2-9larrcolor(red)"in vertex form"`

`rArr-h=2rArrh=-2" and "k=-9`

`"compare with "(x+p)^2+qrArrp=2" and "q=-9`
graph{(y-x^2-4x+5)((x+2)^2+(y+9)^2-0.04)=0 [-20, 20, -10, 10]}