Читать книгу Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice) - Mary Jane Sterling, Mary Sterling Jane - Страница 9
ОглавлениеChapter 2
Solving Quadratic Equations and Nonlinear Inequalities
A quadratic expression is one containing a term raised to the second power. When a quadratic expression is set equal to 0, you have an equation that has the possibility of two real solutions; for example, you may have an equation for which the answers are . Nonlinear inequalities can have an infinite number of solutions, so those answers are written with expressions such as x > 8 or x > –2; these solutions can also be written using interval notation.
The Problems You’ll Work On
In this chapter, you’ll work with quadratic equations and inequalities in the following ways:
Solving simple equations using the square root rule
Rewriting quadratics as the product of two binomials in order to solve them
Applying the quadratic formula
Completing the square
Solving quadratic-like equations
Finding the solutions of quadratic and other nonlinear inequalities
What to Watch Out For
Don’t let common mistakes like the following ones trip you up when working with quadratic equations and inequalities:
Forgetting to consider ±x when using the square root rule
Reducing the fraction incorrectly when applying the quadratic formula
Stopping too soon when solving quadratic-like equations
Eliminating values as solutions when they create a 0 in the denominator of a fraction
Applying the Square Root Rule on Quadratic Equations
51–60 Solve the equations using the square root rule.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
Solving Quadratic Equations Using Factoring
61–76 Solve the quadratic equations by factoring and applying the Multiplication Property of Zero.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
Using the Quadratic Formula to Solve Equations
77–86 Solve the quadratic equations using the quadratic formula.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
Recognizing and Solving Quadratic-Like Equations
87–96 Solve the quadratic-like equations.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
Completing the Square to Solve Quadratic Equations
97–104 Solve the quadratic equations by completing the square.
97.
98.
99.
100.
101.
102.
103.
104.
Combining Methods When Solving Quadratic Equations
105–114 Solve using the most efficient methods.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
Solving Quadratic Inequalities Using Number Lines
115–130 Solve the quadratic inequalities.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
