Evaluate f(10)=1/2x^2+2x-5

$f (10) = \frac{1}{2} x^{2} + 2 x - 5$

Divide each term in $f (10) = \frac{1}{2} x^{2} + 2 x - 5$ by $10$ .

$\frac{f \cdot 10}{10} = \frac{\frac{1}{2} x^{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{f \cdot 10}{10} = \frac{\frac{1}{2} x^{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Divide $f$ by $1$ .

$f = \frac{\frac{1}{2} x^{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Simplify the right side.

Simplify each term.

Combine $\frac{1}{2}$ and $x^{2}$ .

$f = \frac{\frac{x^{2}}{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{x^{2}}{2} \cdot \frac{1}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Combine.

$f = \frac{x^{2} \cdot 1}{2 \cdot 10} + \frac{2 x}{10} + \frac{- 5}{10}$

Multiply $x^{2}$ by $1$ .

$f = \frac{x^{2}}{2 \cdot 10} + \frac{2 x}{10} + \frac{- 5}{10}$

Multiply $2$ by $10$ .

$f = \frac{x^{2}}{20} + \frac{2 x}{10} + \frac{- 5}{10}$

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2 x$ .

$f = \frac{x^{2}}{20} + \frac{2 (x)}{10} + \frac{- 5}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$f = \frac{x^{2}}{20} + \frac{2 x}{2 \cdot 5} + \frac{- 5}{10}$

Cancel the common factor.

$f = \frac{x^{2}}{20} + \frac{2 x}{2 \cdot 5} + \frac{- 5}{10}$

Rewrite the expression.

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{- 5}{10}$

Cancel the common factor of $- 5$ and $10$ .

Factor $5$ out of $- 5$ .

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{5 (- 1)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{5 \cdot - 1}{5 \cdot 2}$

Cancel the common factor.

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{5 \cdot - 1}{5 \cdot 2}$

Rewrite the expression.

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{- 1}{2}$

Move the negative in front of the fraction.

$f = \frac{x^{2}}{20} + \frac{x}{5} - \frac{1}{2}$