Solve f(x)=2(x-6)^2-7

$$f ( x ) = 2 ( x - 6 ) ^ { 2 } - 7$$

Evaluate

$$2\left(x-6\right)^{2}-7$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2\left(x^{2}-12x+36\right)-7$$

Use the distributive property to multiply 2 by x^{2}-12x+36.

$$2x^{2}-24x+72-7$$

Subtract 7 from 72 to get 65.

$$2x^{2}-24x+65$$

Expand

$$2x^{2}-24x+65$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2\left(x^{2}-12x+36\right)-7$$

Use the distributive property to multiply 2 by x^{2}-12x+36.

$$2x^{2}-24x+72-7$$

Subtract 7 from 72 to get 65.

$$2x^{2}-24x+65$$