What is the answer in the picture ?

For a, the function is increasing from (-1, 1) so it is false

for b, (-3,5) includes (-1,1) and it is increasing for at least part of it , so it is false

For c, the function is going up for all the periods mentioned, so it is true!

 b = 4 and c = 7.

Explanation:

Comparing y = x^2+bx+c to y = ax^2+bx+c, we see that a = 1.

The vertex given is (-2,3). In general, the vertex is (h,k). So h = -2 and k = 3.

Plug those three values into the vertex form below

y = a(x-h)^2 + k

y = 1(x-(-2))^2 + 3

y = (x+2)^2 + 3

Then expand everything out and simplify

y = x^2+4x+4 + 3

y = x^2+4x+7

We see that b = 4 and c = 7.