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**Precal**

[tex]f(x)=-4x^2+4x \rightarrow f(x)=a(x-h)^2+k[/tex]

[tex]f(x)=-4(x^2-x)[/tex]

[tex]f(x)=-4\left[x^2-x+\left(\frac 1 2\right)^2-\left(\frac 1 2\right)^2\right][/tex]

[tex]f(x)=-4\left[x^2-x+\left(\frac 1 2\right)^2-\frac 1 4\right][/tex]

[tex]f(x)=-4\left[x^2-x+\left(\frac 1 2\right)^2\right]+1[/tex]

[tex]f(x)=-4\left(x-\frac 1 2\right)^2+1[/tex]

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