write an equation for each parabola?
1. vertex (0,0) ; focus (0, -1/12)
2. vertex (5,1) ; focus (5, 5/4)
3. vertex (1,3) ; directrix x=7/8
at least an explanation and answer for number one would be greatly appreciated!
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1) Vertex ( 0,0 ) , focus ( , -1/12 ) => parabola downward, a symmetry axis x = 0 , the standard form of the parabola : ( x -- h )^2 = 4p ( y - k)
Vertex (h , k) =(0 ,0 ); focus ( h , k + p ) = ( 0 , - 1/12
=> k + p = - 1/12 => p = - 1/12. The equation of the parabola : x^2 = 4 ( - 1/12 ) => x^2 = - 1/3 y
3) Vertex ( 1 , 3 ) and directrix x = 7/8 = h - p =>
p = 1 - 7/8 = 1/8. The parabola opens right, the axis of symmetry is x- axis. The standard form of the parabola : ( y - k )^2 = 4p ( x - h ) =>
( y - 3 )^2 = 1/2 ( x - 1 )
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