Solve f(x)=-1/4(x-12)^2-3

$$f ( x ) = - 1 / 4 ( x - 12 ) ^ { 2 } - 3$$

Evaluate

$$-\frac{\left(x-12\right)^{2}}{4}-3$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-12\right)^{2}.

$$-\frac{1}{4}\left(x^{2}-24x+144\right)-3$$

Use the distributive property to multiply -\frac{1}{4} by x^{2}-24x+144.

$$-\frac{1}{4}x^{2}+6x-36-3$$

Subtract 3 from -36 to get -39.

$$-\frac{1}{4}x^{2}+6x-39$$

Expand

$$-\frac{x^{2}}{4}+6x-39$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-12\right)^{2}.

$$-\frac{1}{4}\left(x^{2}-24x+144\right)-3$$

Use the distributive property to multiply -\frac{1}{4} by x^{2}-24x+144.

$$-\frac{1}{4}x^{2}+6x-36-3$$

Subtract 3 from -36 to get -39.

$$-\frac{1}{4}x^{2}+6x-39$$