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. 
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 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:
{{{ graph( 300, 300, -10,10, -10, 10,(x^2-2x+17)/8) }}}