Textbook Question
Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = √-x is a reflection of the graph of y = √x across the ___-axis.
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem R.6.53
Solve each quadratic equation using the square root property. See Example 6. x² = 16
Verified step by step guidance1
Identify the given quadratic equation: \(x^{2} = 16\).
Recall the square root property, which states that if \(x^{2} = k\), then \(x = \pm \sqrt{k}\).
Apply the square root property to the equation: \(x = \pm \sqrt{16}\).
Simplify the square root: \(x = \pm 4\).
Write the final solution as two values: \(x = 4\) and \(x = -4\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Root Property
The square root property states that if x² = k, then x = ±√k. This means to solve an equation where a variable is squared and set equal to a number, you take the square root of both sides, considering both positive and negative roots.
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Imaginary Roots with the Square Root Property
Solving Quadratic Equations
Quadratic equations are polynomial equations of degree two, often written as ax² + bx + c = 0. When the equation is in the form x² = k, it can be solved directly using the square root property without factoring or using the quadratic formula.
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6:24Solving Quadratic Equations by Completing the Square
Simplifying Square Roots
When taking the square root of a number, it is important to simplify the radical if possible. For example, √16 simplifies to 4. Simplifying helps in finding exact solutions and understanding the nature of the roots.
Recommended video:
2:20Imaginary Roots with the Square Root Property
Related Practice
Textbook Question
CONCEPT PREVIEW Which one is not a linear equation? A. 5x + 7 (x - 1) = -3x B. 9x² - 4x + 3 = 0 C. 7x + 8x = 13 D. 0.04x - 0.08x = 0.40
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Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The numerical coefficient in the term -7yz² is ___________.
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Textbook Question
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. -2x - 2 ≤ 1 + x
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Textbook Question
Solve each quadratic equation using the quadratic formula. See Example 7.
-3x² + 6x + 5 = 0
Textbook Question
Solve each quadratic equation using the zero-factor property. See Example 5. 25x² + 30x + 9 = 0