Solve g(x)=1/2(x-8)^2-8

$$g ( x ) = \frac { 1 } { 2 } ( x - 8 ) ^ { 2 } - 8$$

Evaluate

$$\frac{\left(x-12\right)\left(x-4\right)}{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$\frac{1}{2}\left(x^{2}-16x+64\right)-8$$

Use the distributive property to multiply \frac{1}{2} by x^{2}-16x+64.

$$\frac{1}{2}x^{2}-8x+32-8$$

Subtract 8 from 32 to get 24.

$$\frac{1}{2}x^{2}-8x+24$$

Expand

$$\frac{x^{2}}{2}-8x+24$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$\frac{1}{2}\left(x^{2}-16x+64\right)-8$$

Use the distributive property to multiply \frac{1}{2} by x^{2}-16x+64.

$$\frac{1}{2}x^{2}-8x+32-8$$

Subtract 8 from 32 to get 24.

$$\frac{1}{2}x^{2}-8x+24$$