Solve f(x)=-3(x+4)^2+5

$$f ( x ) = - 3 ( x + 4 ) ^ { 2 } + 5$$

Evaluate

$$-3\left(x+4\right)^{2}+5$$

Solution Steps

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

$$-3\left(x^{2}+8x+16\right)+5$$

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

$$-3x^{2}-24x-48+5$$

Add -48 and 5 to get -43.

$$-3x^{2}-24x-43$$

Expand

$$-3x^{2}-24x-43$$

Solution Steps

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

$$-3\left(x^{2}+8x+16\right)+5$$

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

$$-3x^{2}-24x-48+5$$

Add -48 and 5 to get -43.

$$-3x^{2}-24x-43$$