Question 939999
Find the rule of a quadratic function if it has a minimum value of y=4, an axis of symmetry at x=3 and passes through point (4,-3)
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Vertex form of a parabolic equation: {{{y = a(x - h)^2 + k}}}
With:
x being 4
y being - 3
h being 3, and
k being 4, this becomes: {{{- 3 = a(4 - 3)^2 + 4}}}
- 3 = a + 4
a = - 3 - 4, or - 7
Rule, or equation: {{{highlight_green(y = - 7(x - 3)^2 + 4)}}}

This is IMPOSSIBLE. For a parabola to have a vertex of (3, 4) and pass through the point, (4, - 3), it 
WILL HAVE a MAXIMUM, not a MINIMUM. If it does have a MINIMUM at (3, 4), it will open UPWARDS, and therefore, 
will NEVER pass through the point (4, - 3), which by the way is a point in the 2nd quadrant. In other words,
its range would be {{{y >= 4}}} 

The above equation represents what the problem states, with the exception that the graph will have a MAXIMA
instead of a MINIMA, as stated before.