Answer: C. $368$

Explanation:1. Use the vertex form of a quadratic function: The vertex of the graph $y=f(x)$ is at $(h,k) = (1,7)$. So, the function can be written as $f(x) = a(x-h)^2 + k = a(x-1)^2 + 7$.

2. Use one of the other points to find the value of $a$: The graph passes through $(2,53)$. Substitute $x=2$ and $f(x)=53$: $53 = a(2-1)^2 + 7$ $53 = a(1)^2 + 7$ $53 = a + 7$ $a = 53 - 7 = 46$. So, the function is $f(x) = 46(x-1)^2 + 7$. (We can verify with the point $(-1,191)$: $f(-1) = 46(-1-1)^2+7 = 46(-2)^2+7 = 46(4)+7 = 184+7 = 191$. This matches.)

3. Calculate $f(-2)$: $f(-2) = 46(-2-1)^2 + 7$ $f(-2) = 46(-3)^2 + 7$ $f(-2) = 46(9) + 7$ $f(-2) = 414 + 7 = 421$.

4. Calculate $f(0)$: $f(0) = 46(0-1)^2 + 7$ $f(0) = 46(-1)^2 + 7$ $f(0) = 46(1) + 7$ $f(0) = 46 + 7 = 53$.

5. Calculate $f(-2) - f(0)$: $f(-2) - f(0) = 421 - 53 = 368$.

6. Compare with the given options: [A] $145$ [B] $237$ [C] $368$ [D] $421$ Our result matches option C.

7. Conclusion: The value of $f(-2)-f(0)$ is $368$.