SOLUTION: The parabola with equation {{{y-3=(x-4)^2}}} has it's vertex at (4,3) and passes through (5,4). Find an equation of a different parabola with its vertex at (4,3)that passes through

Here's the graph of  with the vertex (4,3) and 
the point (5,4).



That is a parabola which opens upward.  Let's sketch in one in
green that would have that same vertex(4,3) and pass through 
that same point (5,4). It will have to open to the right.



A parabola which open to the right or left has equation



So we substitute (h,k) = (4,3) 



Now we know that since (x,y) = (5,4) is a point on the
graph, that point must satisfy the equation: 

So






 

Therefore the equartion is found by substituting 

into 

or







Edwin