SOLUTION: Find (a) the directrix, (b) the focus and (c) the roots of the parabola y=x2-5x+4

Question 211314This question is from textbook
: Find (a) the directrix, (b) the focus and (c) the roots of the parabola
y=x2-5x+4 This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find (a) the directrix, (b) the focus and (c) the roots of the parabola
y=x^2-5x+4
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Complete the square:
x^2-5x+? = y-4 +?
x^2-5x + (5/2)^2 = y - 4 + (5/2)^2
(x-(5/2))^2 = y + (9/4)
----------------------------------
Vertex at (5/2 , -9/4)
4p = 1
p = 1/4
---
Focus at (5/2, (-9/4)+(1/4)) = (5/2 , -2)
--------------
Roots:
Solve x^2-5x+4 = 0
Factor:
(x-4)(x-1) = 0
x = 4 ; x = 1
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Cheers.
Stan H.
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