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Question 93472This question is from textbook
: Find the what what and the what? please help me!!! Find (a)the directrix,
(b) the focus and (c) the roots of the parabola y = x^2 - 5x + 4
(a)_________________
(b)_________________
(c)_________________
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 on the x terms and keep the equation balanced:
x^2 - 5x + 4 = y
x^2 -5x + ? = y-4 + ?
x^2 + 5x + (5/2)^2 = y - 16/4 + (25/4)
Factor and simplify to get:
(x+(5/2))^2 = (y+9/4)
Note: This follows the form (x-h)^2 = 4P(y-k)
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a) directrix is x = -5/2
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b) 4P=1; p=1/4
Vertex is (-5/2 , -9/4)
Focus is (-5/2 , -9/4 + 1/4) = (-5/2 , -2)
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c) Roots:
y = x^2 - 5x + 4
Let y=0 and solve for x:
x^2-5x+4 = 0
(x-4)(x-1) = 0
x=4 or x=1
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Cheers,
Stan H.
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