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

$$f ( x ) = - \frac { 1 } { 4 } ( x + 3 ) ^ { 2 } - 4$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$-\frac{1}{4}\left(x^{2}+6x+9\right)-4$$

Use the distributive property to multiply -\frac{1}{4} by x^{2}+6x+9.

$$-\frac{1}{4}x^{2}-\frac{3}{2}x-\frac{9}{4}-4$$

Subtract 4 from -\frac{9}{4} to get -\frac{25}{4}.

$$-\frac{1}{4}x^{2}-\frac{3}{2}x-\frac{25}{4}$$

Expand

$$-\frac{x^{2}}{4}-\frac{3x}{2}-\frac{25}{4}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$-\frac{1}{4}\left(x^{2}+6x+9\right)-4$$

Use the distributive property to multiply -\frac{1}{4} by x^{2}+6x+9.

$$-\frac{1}{4}x^{2}-\frac{3}{2}x-\frac{9}{4}-4$$

Subtract 4 from -\frac{9}{4} to get -\frac{25}{4}.

$$-\frac{1}{4}x^{2}-\frac{3}{2}x-\frac{25}{4}$$