For the following exercises, rewrite the quadratic functions in standard form and give the vertex. $h(x)=2 x^{2}+8 x-10$

Represent the number you would have to add to an expression of the form $x ^ { 2 } + b x$ to make a complete square.

For the following exercises, simplify the expression.\

$$\left(\frac{16 a^3}{b^2}\right)\left(4 a b^{-1}\right)^{-2}$$

For the following exercises, simplify the given expression. Write answers with positive exponents. $\left(b^{-3} c\right)^{3}$

For the following exercises, find $(f \circ g)(x)$ and $(g \circ f)(x)$ for each pair of functions.\

$$f(x)=\sqrt{x+2}, g(x)=\frac{1}{x}$$

For the following exercises, determine the domain for each function in interval notation. Given $f(x)=\sqrt{x}$ and g(x)=|x - 3|, find $\frac{g}{f}.$

Add or subtract as indicated.

$$\frac{5}{y}+\frac{2}{y+1}-\frac{6}{y^2}$$

Add or subtract as indicated. Simplify each answer.

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

Add.

$$\frac{2}{5}+\frac{1}{3}+\frac{7}{10}=$$

Why do you think Conrad chose to have Arsat narrate his own story?

Solve each equation. See the examples in this chapter. (A few exercises are linear equations.)

$$x^2+22 x+121=0$$

For the following exercises, factor the polynomial.\

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

For the following exercises, find the product. $\left(6 b^{2}-6\right)\left(4 b^{2}-4\right)$

Add or subtract. Write the expression in standard form.

$$(9z^2+28)-(z^2+8z-8)$$