An absolute value equation is an equation that contains an absolute value expression. The absolute value of a number is its distance from zero on a number line. In an absolute value equation, the variable can have two possible values that satisfy the equation.
To solve an absolute value equation, you must first isolate the absolute value expression on one side of the equation. Then, split the equation into two separate equations, one with the positive value of the absolute value expression and one with the negative value. Solve each equation separately to find the possible values of the variable.
A quadratic equation is an equation with the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The difference between two quadratics is that they have different values for the constants a, b, and c. This leads to different shapes and positions of the parabolas.
To solve a quadratic equation, you can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. You can also factor the equation or complete the square to solve for the variable.
Absolute value equations can be used to solve problems involving distance, speed, and time. For example, if you are traveling at a constant speed and need to know how long it will take to reach a destination, you can use an absolute value equation to solve for the possible times. Additionally, absolute value equations can be used in physics to solve problems involving acceleration and displacement.