Question

What do solving absolute value equations and solving quadratic equations have in common?

Answer 1

Answer:

Step-by-step explanation:

Quadratic equations are equations that when rearranged using the 5 operations can yield a polynomial of degree 2 on one side of the equation and 0 on the other. There are 3 commonly taught methods for solving quadratic equations. These methods are factoring, completing the square, and the quadratic formula. These functions are most commonly used to model projectiles, disregarding air resistance.

When using the factoring method one attempts to write a degree 2 polynomial as the product of two degree 1 polynomials. This method works because if we multiply two degree one polynomials together we find  

For example: When factoring , we want to find two number a, b whose product is 6 and sum to 5. The values of a and b we are looking for are 2 and 3.

The method of completing the square centers around using the five operations to replace the original equation with an equivalent equation of the form  by taking advantage of the fact that

The absolute value function takes the value of a number, regardless of whether it is positive or negative. Some problems that the absolute value is useful for modeling include an object bouncing on the ground.

For example, , since we do not care about the negative sign.

Example: Solve  

Solution: Since the absolute value does not care about whether a number is positive or negative, if  then  or . Then we can solve each equation individually to find that x = 1 or 5.

Answer 2

Answer:

They often have more than one solution.