Solve f(x)=-8(x-5)^2-4

$$f ( x ) = - 8 ( x - 5 ) ^ { 2 } - 4$$

Evaluate

$$-8\left(x-5\right)^{2}-4$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$-8\left(x^{2}-10x+25\right)-4$$

Use the distributive property to multiply -8 by x^{2}-10x+25.

$$-8x^{2}+80x-200-4$$

Subtract 4 from -200 to get -204.

$$-8x^{2}+80x-204$$

Expand

$$-8x^{2}+80x-204$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$-8\left(x^{2}-10x+25\right)-4$$

Use the distributive property to multiply -8 by x^{2}-10x+25.

$$-8x^{2}+80x-200-4$$

Subtract 4 from -200 to get -204.

$$-8x^{2}+80x-204$$