Domanda del libro di testo
Use interval notation to represent all values of x satisfying the given conditions. y = |2x - 5| + 1 and y > 9
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 101
Exercises 100–102 will help you prepare for the material covered in the next section. Factor:
Guida verificata passo dopo passo1
Recognize that the quadratic expression is in the form \(x^2 - 6x + 9\), which is a trinomial that might be a perfect square.
Recall the perfect square trinomial formula: \((a - b)^2 = a^2 - 2ab + b^2\).
Identify \(a\) and \(b\) such that \(a^2 = x^2\) and \(b^2 = 9\), so \(a = x\) and \(b = 3\).
Check if the middle term \(-6x\) matches \(-2ab = -2 \times x \times 3 = -6x\), which it does.
Write the factored form as \((x - 3)^2\).
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Factoring Quadratic Expressions
Factoring quadratics involves rewriting a quadratic expression as a product of two binomials. This process helps simplify expressions and solve equations. Recognizing patterns like perfect square trinomials or using methods such as factoring by grouping is essential.
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Solving Quadratic Equations by Factoring
Perfect Square Trinomials
A perfect square trinomial is a quadratic expression that can be written as the square of a binomial, typically in the form a^2 ± 2ab + b^2 = (a ± b)^2. Identifying this pattern allows quick factoring without trial and error.
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06:24Solving Quadratic Equations by Completing the Square
Using the Quadratic Formula or Completing the Square
When factoring is not straightforward, the quadratic formula or completing the square can find roots of the quadratic. These roots help express the quadratic as a product of linear factors, aiding in factoring and solving equations.
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06:24Solving Quadratic Equations by Completing the Square
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