Solve f(x)=1/4(x+2)^2-5

$$f ( x ) = \frac { 1 } { 4 } ( x + 2 ) ^ { 2 } - 5$$

Evaluate

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

Solution Steps

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

$$\frac{1}{4}\left(x^{2}+4x+4\right)-5$$

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

$$\frac{1}{4}x^{2}+x+1-5$$

Subtract 5 from 1 to get -4.

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

Expand

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

Solution Steps

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

$$\frac{1}{4}\left(x^{2}+4x+4\right)-5$$

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

$$\frac{1}{4}x^{2}+x+1-5$$

Subtract 5 from 1 to get -4.

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