Chapter 2

Solve the inequality algebraically or graphically. $$-2 x^{2}+2 x+3 \geq 0$$

Solve the rational equation. Check your solutions. $$\frac{x-1}{3 x+3}-\frac{9}{x^{2}-1}=\frac{2}{x+1}$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$h(x)=x^{2}-4 x+6$$

Find the complex conjugate of each number. $$9-\sqrt{3}$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$(f h)(1)$$

Solve the quadratic equation by completing the square. $$x^{2}-6 x=7$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=|3 x|-2$$

Solve the inequality algebraically or graphically. $$x^{2}+1<0$$

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x+3}=5$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$w(x)=-x^{2}+6 x+4$$

Find the complex conjugate of each number. $$i^{2}$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$\left(\frac{f}{g}\right)(-2)$$

Solve the quadratic equation by completing the square. $$x^{2}-2 x=4$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=(x+1)^{2}$$

Solve the inequality algebraically or graphically. $$-x^{2}-4>0$$

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x+2}=6$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$f(x)=-x^{2}-4 x+5$$

Find the complex conjugate of each number. $$i^{3}$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$\left(\frac{f}{g}\right)(3)$$

Solve the quadratic equation by completing the square. $$x^{2}+8 x=6$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=-3 x^{2}+1$$

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x^{2}+1}=\sqrt{17}$$

Solve the inequality algebraically or graphically. $$x^{2}+2 x+1 \geq 0$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$h(x)=x^{2}+x-3$$

Find \(x+y, x-y, x y,\) and \(x / y\). $$x=3 i ; y=2-i$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$\left(\frac{g}{h}\right)(3)$$

Solve the quadratic equation by completing the square. $$x^{2}+x=2$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=-x^{3}+1$$

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x^{2}+3}=\sqrt{28}$$

Solve the inequality algebraically or graphically. $$x^{2}-x+1 \geq 0$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$g(x)=-x^{2}+x-7$$

Find \(x+y, x-y, x y,\) and \(x / y\). $$x=-2 i ; y=5+i$$

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$\left(\frac{g}{h}\right)(-2)$$

Solve the quadratic equation by completing the square. $$x^{2}-x=3$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=-|x|+1$$

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x^{2}+6 x}-1=3$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$f(x)=3 x^{2}+6 x-4$$

Find \(x+y, x-y, x y,\) and \(x / y\). $$x=-3+5 i ; y=2-3 i$$

Use the verbal description to find an algebraic expression for the function. The graph of the function \(g(t)\) is formed by translating the graph of \(f(t)=|t| 4\) units to the left and 3 units down.

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$\left(\frac{f}{h}\right)(1)$$

Solve the quadratic equation by completing the square. $$2 x^{2}+8 x-1=0$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=2 x$$

Write each quadratic function in the form \(f(x)=a(x-h)^{2}+k\) by completing the square. Also find the vertex of the associated parabola and determine whether it is a maximum or minimum point. $$f(x)=-2 x^{2}+8 x+3$$

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x^{2}-5 x}+4=10$$

The price \(s\) (in dollars) of a product is given by \(s(q)=100-0.1 q, 0 \leq q \leq 1000,\) where \(q\) is the number of units sold per day. It costs \(\$ 10,000\) per day to operate the factory and an additional \(\$ 12\) for each unit produced. (a) Find the daily revenue function, \(R(q)\) (b) Find the daily cost function, \(C(q)\) (c) The profit function is given by \(P(q)=R(q)-C(q)\) For what values of \(q\) will the profit be greater than or equal to zero?

Find \(x+y, x-y, x y,\) and \(x / y\). $$x=2-9 i ; y=-4+6 i$$

Use the verbal description to find an algebraic expression for the function. The graph of the function \(f(t)\) is formed by translating the graph of \(h(t)=t^{2} 2\) units to the right and 6 units upward.

In Exercises \(17-40,\) let \(f(x)=-x^{2}+x, g(x)=\frac{2}{x+1},\) and \(h(x)=-2 x+1 .\) Evaluate each of the following. $$\left(\frac{h}{f}\right)(2)$$

Solve the quadratic equation by completing the square. $$3 x^{2}-6 x+2=0$$

Decide if each function is odd, even, or neither by using the definitions. $$f(x)=|x-1|$$