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
Daniel Tan
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#

Jim G.
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]}

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