Question 455843
write the standard form of the equation of the parabola with its vertex at (0,0) and focus at (-2,0)
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From given info, it can be seen that this is a parabola with a horizontal axis of symmetry, y=0 or x-axis, and it opens leftward. You can tell it has a horizontal axis of symmetry because the y-coordinates of the focus and vertex are the same.  It opens leftward because the focus is to the left of the vertex. Because it opens leftwards, the function has a negative sign.
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Standard form of given parabola: 
(y-k)^2=-4p(x-h)
(y-0)^2=-4p(x-0)
y^2=-4px
p=distance between vertex and focus on the axis of symmetry=2
4p=8
Equation: y^2=-8x
See the graph below as a visual check on the answer.
y=(-8x)^.5
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{{{ graph( 300, 300, -10, 10, -10, 10,(-8x)^.5,-(-8x)^.5) }}}