Solve -3(x-1/2)^2+11/4

$$- 3 ( x - \frac { 1 } { 2 } ) ^ { 2 } + \frac { 11 } { 4 }$$

Evaluate

$$\frac{-3\left(2x-1\right)^{2}+11}{4}$$

Solution Steps

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

$$-3\left(x^{2}-x+\frac{1}{4}\right)+\frac{11}{4}$$

Use the distributive property to multiply -3 by x^{2}-x+\frac{1}{4}.

$$-3x^{2}+3x-\frac{3}{4}+\frac{11}{4}$$

Add -\frac{3}{4} and \frac{11}{4} to get 2.

$$-3x^{2}+3x+2$$

Expand

$$2+3x-3x^{2}$$

Solution Steps

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

$$-3\left(x^{2}-x+\frac{1}{4}\right)+\frac{11}{4}$$

Use the distributive property to multiply -3 by x^{2}-x+\frac{1}{4}.

$$-3x^{2}+3x-\frac{3}{4}+\frac{11}{4}$$

Add -\frac{3}{4} and \frac{11}{4} to get 2.

$$-3x^{2}+3x+2$$