Solve f(x)=-2(x-1/2)^2+4/5

$$f ( x ) = - 2 ( x - \frac { 1 } { 2 } ) ^ { 2 } + \frac { 4 } { 5 }$$

Evaluate

$$-\frac{\left(2x-1\right)^{2}}{2}+\frac{4}{5}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}\right)^{2}.

$$-2\left(x^{2}-x+\frac{1}{4}\right)+\frac{4}{5}$$

Use the distributive property to multiply -2 by x^{2}-x+\frac{1}{4}.

$$-2x^{2}+2x-\frac{1}{2}+\frac{4}{5}$$

Add -\frac{1}{2} and \frac{4}{5} to get \frac{3}{10}.

$$-2x^{2}+2x+\frac{3}{10}$$

Expand

$$\frac{3}{10}+2x-2x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}\right)^{2}.

$$-2\left(x^{2}-x+\frac{1}{4}\right)+\frac{4}{5}$$

Use the distributive property to multiply -2 by x^{2}-x+\frac{1}{4}.

$$-2x^{2}+2x-\frac{1}{2}+\frac{4}{5}$$

Add -\frac{1}{2} and \frac{4}{5} to get \frac{3}{10}.

$$-2x^{2}+2x+\frac{3}{10}$$