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

2 Answers
May 1, 2018

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

May 1, 2018

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]}