1. **State the problem:** We want to find the value of $c$ such that the graphs of the two functions $$y = 2x^2 - 36x + c$$ and $$y = 2(x - 9)^2 - 18$$ are the same. 2. **Recall the formula and rules:** Two functions are the same if their expressions are equivalent for all $x$. 3. **Expand the second function:** $$2(x - 9)^2 - 18 = 2(x^2 - 18x + 81) - 18 = 2x^2 - 36x + 162 - 18 = 2x^2 - 36x + 144$$ 4. **Set the two expressions equal:** $$2x^2 - 36x + c = 2x^2 - 36x + 144$$ 5. **Compare the constant terms:** Since the coefficients of $x^2$ and $x$ are the same, the constants must be equal: $$c = 144$$ **Final answer:** $c = 144$