The graph of the quadratic y = ax^2 + bx + c has the following properties: (1) The maximum value of y = ax^2 + bx + c is 5, which occurs at x = 3. (2) The graph passes through the point (0,8). If the graph passes through the point (4,m), then what is the value of m?
+592 5 = 9a+3b+c
8 = 0 + 0 + c
c=8
-3 = 9a + 3b
m = 16a+4b+8
m-8 = 16a + 4b
m-5 = 7a +b
3b = -9a - 3
b=-3a-1
m = 5 + 4a-1 = 4a+4
m=a2^2+b2+8
2b+8=4
b=-2
a=1/3
m=4+4/3=$\boxed{\dfrac{16}3}$
+592 5 = 9a+3b+c
8 = 0 + 0 + c
c=8
-3 = 9a + 3b
m = 16a+4b+8
m-8 = 16a + 4b
m-5 = 7a +b
3b = -9a - 3
b=-3a-1
m = 5 + 4a-1 = 4a+4
m=a2^2+b2+8
2b+8=4
b=-2
a=1/3
m=4+4/3=$\boxed{\dfrac{16}3}$
