SOLUTION: Find (a)the directix,(b)the focus and (c)the roots of the parabola y=x^2-5x+4

Question 41140This question is from textbook Algebra and Trigonometry
: Find (a)the directix,(b)the focus and (c)the roots of the parabola y=x^2-5x+4 This question is from textbook Algebra and Trigonometry

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Find (a)the directix,(b)the focus and (c)the roots of the parabola y=x^2-5x+4
Y=(X^2-2*X*2.5+2.5^2)+4-2.5^2
Y=(X-2.5)^2-2.25
(Y+2.25)=(X-2.5)^2
COMPARING WITH STD.EQN.OF
4A(Y-K)=(X-H)^2,WE GET
VERTEX IS (H,K)....(2.5,-2.25)
4A=1....OR...A=0.25
FOCUS IS (H,K+A).....(2.5,-2.25+0.25)=(2.5,-2)
DIRECTRIX IS Y-K+A=0..........Y+2.25+0.25=Y+2.5=0
ROOTS ARE
X^2-5X+4=0
X^2-4X-X+4=0
X(X-4)-1(X-4)=0
(X-1)(X-4)=0
X=1...OR....4.
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