Solve f(x)=-8/3(x-1)^2+32/3

$$f ( x ) = - \frac { 8 } { 3 } ( x - 1 ) ^ { 2 } + \frac { 32 } { 3 }$$

Evaluate

$$-\frac{8\left(x-3\right)\left(x+1\right)}{3}$$

Solution Steps

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

$$-\frac{8}{3}\left(x^{2}-2x+1\right)+\frac{32}{3}$$

Use the distributive property to multiply -\frac{8}{3} by x^{2}-2x+1.

$$-\frac{8}{3}x^{2}+\frac{16}{3}x-\frac{8}{3}+\frac{32}{3}$$

Add -\frac{8}{3} and \frac{32}{3} to get 8.

$$-\frac{8}{3}x^{2}+\frac{16}{3}x+8$$

Expand

$$-\frac{8x^{2}}{3}+\frac{16x}{3}+8$$

Solution Steps

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

$$-\frac{8}{3}\left(x^{2}-2x+1\right)+\frac{32}{3}$$

Use the distributive property to multiply -\frac{8}{3} by x^{2}-2x+1.

$$-\frac{8}{3}x^{2}+\frac{16}{3}x-\frac{8}{3}+\frac{32}{3}$$

Add -\frac{8}{3} and \frac{32}{3} to get 8.

$$-\frac{8}{3}x^{2}+\frac{16}{3}x+8$$