Evaluate
-\frac{\left(4x-1\right)^{2}}{16}+2
Expand
-x^{2}+\frac{x}{2}+\frac{31}{16}
Graph
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-\left(x^{2}-\frac{1}{2}x+\frac{1}{16}\right)+4\times \frac{1}{4}+1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{4}\right)^{2}.
-x^{2}+\frac{1}{2}x-\frac{1}{16}+4\times \frac{1}{4}+1
To find the opposite of x^{2}-\frac{1}{2}x+\frac{1}{16}, find the opposite of each term.
-x^{2}+\frac{1}{2}x-\frac{1}{16}+1+1
Multiply 4 and \frac{1}{4} to get 1.
-x^{2}+\frac{1}{2}x+\frac{15}{16}+1
Add -\frac{1}{16} and 1 to get \frac{15}{16}.
-x^{2}+\frac{1}{2}x+\frac{31}{16}
Add \frac{15}{16} and 1 to get \frac{31}{16}.
-\left(x^{2}-\frac{1}{2}x+\frac{1}{16}\right)+4\times \frac{1}{4}+1
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{4}\right)^{2}.
-x^{2}+\frac{1}{2}x-\frac{1}{16}+4\times \frac{1}{4}+1
To find the opposite of x^{2}-\frac{1}{2}x+\frac{1}{16}, find the opposite of each term.
-x^{2}+\frac{1}{2}x-\frac{1}{16}+1+1
Multiply 4 and \frac{1}{4} to get 1.
-x^{2}+\frac{1}{2}x+\frac{15}{16}+1
Add -\frac{1}{16} and 1 to get \frac{15}{16}.
-x^{2}+\frac{1}{2}x+\frac{31}{16}
Add \frac{15}{16} and 1 to get \frac{31}{16}.
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