Solve g(x)=-3(x-4)^2-2

$$g ( x ) = - 3 ( x - 4 ) ^ { 2 } - 2$$

Evaluate

$$-3\left(x-4\right)^{2}-2$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$-3\left(x^{2}-8x+16\right)-2$$

Use the distributive property to multiply -3 by x^{2}-8x+16.

$$-3x^{2}+24x-48-2$$

Subtract 2 from -48 to get -50.

$$-3x^{2}+24x-50$$

Expand

$$-3x^{2}+24x-50$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$-3\left(x^{2}-8x+16\right)-2$$

Use the distributive property to multiply -3 by x^{2}-8x+16.

$$-3x^{2}+24x-48-2$$

Subtract 2 from -48 to get -50.

$$-3x^{2}+24x-50$$