Solve f(x)=-3(x-5)^2-1

$$f ( x ) = - 3 ( x - 5 ) ^ { 2 } - 1$$

Evaluate

$$-3\left(x-5\right)^{2}-1$$

Solution Steps

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

$$-3\left(x^{2}-10x+25\right)-1$$

Use the distributive property to multiply -3 by x^{2}-10x+25.

$$-3x^{2}+30x-75-1$$

Subtract 1 from -75 to get -76.

$$-3x^{2}+30x-76$$

Expand

$$-3x^{2}+30x-76$$

Solution Steps

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

$$-3\left(x^{2}-10x+25\right)-1$$

Use the distributive property to multiply -3 by x^{2}-10x+25.

$$-3x^{2}+30x-75-1$$

Subtract 1 from -75 to get -76.

$$-3x^{2}+30x-76$$