find a b and c please

Question

The graph of the function

f(x)=ax^2+bx+c

has its vertex at (0, 5)

and passes through the point (1, 6). 

 

Find​ a, b, and c.

Answer 1

f(0) = a(0) + b(0) + c

5 = a(0) + b(0) + c

c = 5

6 = a + b + 5

1 = a + b

f(x) also passes through (-1, 6) by symmetry

6 = a - b + 5 add this to 1 = a + b

7 = 2a + 5

2 = 2a

1 = a

0 = b