Ans: C
A may not be true. The function $f(x)=\dfrac{1}{2}(x-3)^2-4$ has the vertex $(3,-4)$, but the roots of $f(x)=0$ are $5.83$ and $0.172$, correct to 3 sig. fig., which are not integers.
A may not be true. The function $f(x)=\dfrac{1}{2}(x-3)^2-4$ has the vertex $(3,-4)$, but the roots of $f(x)=0$ are $5.83$ and $0.172$, correct to 3 sig. fig., which are not integers.
B may not be true. The function $f(x)=-(x-3)^2-4$ has the vertex $(3,-4)$, but $f(x)-3=0$ has no real roots.
C must be true. The function $f(x)=a(x-3)^2-4$ has the vertex $(3,-4)$, and the roots of $f(x)+4=0$ are $3$.
D may not be true. The function $f(x)=-(x-3)^2-4$ has the vertex $(3,-4)$, but the roots of $f(x)+5=0$ are $2$ and $4$.
