Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
The Quadratic Formula
6:39 minutes
Problem 103
Textbook Question
Textbook QuestionIn Exercises 101–106, solve each equation. |x^2 + 2x - 36| = 12
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
6mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is defined as |x| = x if x ≥ 0 and |x| = -x if x < 0. In the context of equations, it creates two separate cases to consider, as the expression inside the absolute value can be either positive or negative.
Recommended video:
7:12
Parabolas as Conic Sections Example 1
Quadratic Equations
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. The solutions to quadratic equations can be found using various methods, including factoring, completing the square, or applying the quadratic formula. Understanding how to manipulate and solve these equations is crucial for solving problems involving absolute values.
Recommended video:
05:35
Introduction to Quadratic Equations
Case Analysis
Case analysis is a problem-solving technique used to break down complex problems into simpler, manageable parts. In the context of absolute value equations, it involves creating separate equations for each possible case (positive and negative) derived from the absolute value expression. This method allows for a systematic approach to finding all possible solutions to the original equation.
Recommended video:
6:02
Stretches & Shrinks of Functions
Watch next
Master Solving Quadratic Equations Using The Quadratic Formula with a bite sized video explanation from Callie
Start learningRelated Videos
Related Practice