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Question 915680: Find (a) the directrix, (b) the focus and (c) the roots of the parabola y=x^2-5x+4.
Help.
Thank you.
Answer by lwsshak3(11628)   (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.
complete the square:
y=(x^2-5x+25/4)-25/4+4
y=(x-5/2)^2-9/4
(x-5/2)^2=(y+9/4)
This is an equation of a parabola that opens up.
Its basic form of equation: (x-h)^2=4p(y-k), (h,k)=coordinates of the vertex
For given equation:(x+(5/2))^2=(y+(9/4))
vertex:(5/2,-9/4)
axis of symmetry: x=5/2
4p=1
p=1/4
a)directrix:y=-10/4=-5/2
b)focus: (5/2,-2)
c) roots:
set y=0
(x-5/2)^2=(y+9/4)
(x-5/2)^2=9/4
x-5/2=±√(9/4)=±3/2
x=5/2±3/2
x=8/2=4
or
x=2/2=1
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