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Solve equations graphically

Let f(x)=x+3xf(x)=x+3^x and let g(x)=−0.5(x+2)2+4g(x)=-0.5(x+2)^2+4.
The graph of y=f(x)y=f(x) is shown below.
Use the interactive graph to sketch a graph of y=g(x)y=g(x).
Created with RaphaëlCreated with Raphaël
Created with Raphaël
Created with Raphaël
Created with Raphaël
Created with Raphaël
1\small{1}2\small{2}3\small{3}4\small{4}5\small{5}6\small{6}7\small{7}8\small{8}9\small{9}-2\small{\llap{-}2}-3\small{\llap{-}3}-4\small{\llap{-}4}-5\small{\llap{-}5}-6\small{\llap{-}6}-7\small{\llap{-}7}-8\small{\llap{-}8}-9\small{\llap{-}9}1\small{1}2\small{2}3\small{3}4\small{4}5\small{5}6\small{6}7\small{7}8\small{8}9\small{9}-2\small{\llap{-}2}-3\small{\llap{-}3}-4\small{\llap{-}4}-5\small{\llap{-}5}-6\small{\llap{-}6}-7\small{\llap{-}7}-8\small{\llap{-}8}-9\small{\llap{-}9}yyxx
Let x1x_1 and x2x_2 be solutions of x+3x=−0.5(x+2)2+4x+3^x=-0.5(x+2)^2+4, where x1>x2x_1>x_2.
Estimate the value of x1x_1.
Answers within 0.5\textit{0.5} units of the solution will be accepted.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}