Graph the Function

The graph of the function f (x) = ax^2 + bx + c has vertex at (1, 5) and passes through the point (2, 7). Find the following.

a =-2/3 b =8/3 c = 13/3

Those are my answer but I am not sure if I got them Correctly

One Answer:
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x-coordinate of vertex is -b/(2a)

-b/(2a)=1

-b=2a

b=-2a

plug in (1,5):

a+b+c=5

plug in (2,7)

4a+2b+c=7

thus

3a+b=2

a=2

b=-4

c=7

this graph shows that y=2x^2-4x+7 has the desired properties:

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