The graph of y=ax²+c has its vertex at (0,4) and passes through the point (3,-5). Find the value of a.?

The vertex of the graph has its vertex at (0, 4).
Hence, the equation of the graph is: y = ax² + 4

The graph passes through the point (3, -5).
Hence, plug x = 3 and y = -5 into the equation:
(-5) = a(3)² + 4
9a + 4 = -5
9a = -9
a = -1

If the vertex is at (0, 4) we have:

4 = a(0)² + c

so, c = 4

Hence, y = ax² + 4

As it passes through (3, -5) we have:

-5 = a(3)² + 4

so, a = -1

Therefore, y = -x² + 4 or 4 - x²

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