Question 88156
Can you write the equation of a parabola when given only the coordinates of the vertex?
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No.  The equation of a parabola is 

f(x) = a(x - h)² + k

where (h,k) = the vertex.  However, the smaller the value of |a|,
the wider the parabola and the larger the value of |a|, the narrower.
When "a" is a positive number, the parabola opens upward. When "a" 
is negative the parabola opens downward.   

Here are five different parabolas, all with the same vertex 
(h,k) = (3,-2) but with different values of "a".

{{{graph(400,400,-10,10,-10,10,(x-3)^2-2, 2(x-3)^2/13-2, -3(x-3)^2-2 , 4(x-3)^2-2,-(x-3)^2/7-2   )}}}

Edwin</pre>