Evaluate
\frac{\left(x+3\right)^{2}}{2}+1
Expand
\frac{x^{2}}{2}+3x+\frac{11}{2}
Graph
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\frac{1}{2}\left(x^{2}+6x+9\right)+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
\frac{1}{2}x^{2}+3x+\frac{9}{2}+1
Use the distributive property to multiply \frac{1}{2} by x^{2}+6x+9.
\frac{1}{2}x^{2}+3x+\frac{11}{2}
Add \frac{9}{2} and 1 to get \frac{11}{2}.
\frac{1}{2}\left(x^{2}+6x+9\right)+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.
\frac{1}{2}x^{2}+3x+\frac{9}{2}+1
Use the distributive property to multiply \frac{1}{2} by x^{2}+6x+9.
\frac{1}{2}x^{2}+3x+\frac{11}{2}
Add \frac{9}{2} and 1 to get \frac{11}{2}.
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