3. a) Graph the function $f(x)=-2(x+1)^{2}+3$
b) Evaluate $f(-3)$
c) What does $f(-3)$ represent on the graph of $f$ ?
d) Use the equation to determine i) $f(1)-f(0)$,
ii) $3 f(2)-5$, and iii) $f(2-x)$

Step 1 ：First, we evaluate $f(-3)$ by substituting $-3$ into the function $f(x)=-2(x+1)^{2}+3$. This gives us $f(-3)=-2((-3)+1)^{2}+3=-2(-2)^{2}+3=-2(4)+3=-8+3=-5$.

Step 2 ：So, $f(-3) = \boxed{-5}$.

Step 3 ：$f(-3)$ represents the y-coordinate of the point on the graph where $x=-3$.

Step 4 ：Next, we calculate $f(1)-f(0)$. We first find $f(1)=-2(1+1)^{2}+3=-2(2)^{2}+3=-2(4)+3=-8+3=-5$ and $f(0)=-2(0+1)^{2}+3=-2(1)+3=-2+3=1$. So, $f(1)-f(0)=-5-1=-6$.

Step 5 ：So, $f(1)-f(0) = \boxed{-6}$.

Step 6 ：Then, we calculate $3f(2)-5$. We first find $f(2)=-2(2+1)^{2}+3=-2(3)^{2}+3=-2(9)+3=-18+3=-15$. So, $3f(2)-5=3(-15)-5=-45-5=-50$.

Step 7 ：So, $3f(2)-5 = \boxed{-50}$.

Step 8 ：Finally, we calculate $f(2-x)$. We substitute $2-x$ into the function $f(x)=-2(x+1)^{2}+3$ to get $f(2-x)=-2((2-x)+1)^{2}+3=-2((2-x)+1)^{2}+3=-2(3-x)^{2}+3$.

Step 9 ：So, $f(2-x) = \boxed{-2(3-x)^{2}+3}$.