SOLUTION: Given the equation x2 � 2x + 1 = 8y � 16. a) Write the equation of the parabo

Question 975225: Given the equation x2 � 2x + 1 = 8y � 16.
a) Write the equation of the parabola in standard form.
b) State the coordinates of the vertex.
c) State the coordinates of the focus.
d) State the equation of the directrix.

e) Sketch the graph.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Given the equation x2 � 2x + 1 = 8y � 16.
a) Write the equation of the parabola in standard form.
b) State the coordinates of the vertex.
c) State the coordinates of the focus.
d) State the equation of the directrix.
***
x^2 � 2x + 1 = 8y � 16.
complete the square:
(x^2-2x+1)=8y-16-1+1
(x-1)^2=8y-16
(x-1)^2=8(y-2)
This is an equation of a parabola that opens upward.
Its basic form of equation: (x-h)^2=4p(y-k), (h,k)=coordinates of the vertex
For given parabola:
vertex: (1, 2)
axis of symmetry: x=-1
4p=8
p=2
focus: (1, 4) (p-units above vertex on the axis of symmetry)
directrix: y=0 (p-units below vertex on the axis of symmetry)
y=(x^2-2x+17)/8
see graph below:

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