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There are a couple of different ways you could do this, but I'll show the simpler way. We will use the formula
along with the fact that the vertex has h and k coordinates of 1 and 4 respectively, and that a point on the graph is (3, 5). We could have used any point on the graph where there is a definite integer coordinate pair. We will fill in accordingly and solve for a.
and
5 = 4a + 4. If we subtract 4 from both sides we get that . Now we will fill in the formula and expand as needed:
and
. If we distribute the 1/4 in and then add the constants the final equation for that graph will be