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

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

Evaluate

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

Solution Steps

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

$$\frac{1}{4}\left(x^{2}+10x+25\right)+2$$

Use the distributive property to multiply \frac{1}{4} by x^{2}+10x+25.

$$\frac{1}{4}x^{2}+\frac{5}{2}x+\frac{25}{4}+2$$

Add \frac{25}{4} and 2 to get \frac{33}{4}.

$$\frac{1}{4}x^{2}+\frac{5}{2}x+\frac{33}{4}$$

Expand

$$\frac{x^{2}}{4}+\frac{5x}{2}+\frac{33}{4}$$

Solution Steps

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

$$\frac{1}{4}\left(x^{2}+10x+25\right)+2$$

Use the distributive property to multiply \frac{1}{4} by x^{2}+10x+25.

$$\frac{1}{4}x^{2}+\frac{5}{2}x+\frac{25}{4}+2$$

Add \frac{25}{4} and 2 to get \frac{33}{4}.

$$\frac{1}{4}x^{2}+\frac{5}{2}x+\frac{33}{4}$$