FACTORING QUADRATIC EQUATION

Standard Form of Quadratic Equation

Above is the standard form of the quadratic equation. The power "2" in "x" as the variable is the indicator that the equation is in the second order thus quadratic. The letters, in color, are the numerical coefficient and constant (c = 5). Being basic in quadratic, let us be reminded that the equation involves both "+" and "-" to separate the term. A term is an Algebraic expression, not an equation. There are like and unlike terms in an equation. Below are the simple illustrations of like and unlike terms.

The quadratic equation is a mathematical formula that is used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. The quadratic equation has a wide range of uses in various fields of study, including:

1. Solving problems in physics and engineering: The quadratic equation is used to solve problems in physics and engineering that involve motion, acceleration, velocity, and distance. For example, the quadratic equation can be used to determine the trajectory of a projectile, the maximum height reached by a ball thrown into the air, or the time it takes for a car to come to a stop.

2. Analyzing financial data: The quadratic equation is used in financial analysis to model and analyze data related to investments, interest rates, and financial forecasting. For example, the quadratic equation can be used to calculate the yield on a bond, the break-even point for a business, or the optimal price for a product.

3. Solving geometric problems: The quadratic equation is used in geometry to solve problems related to areas, volumes, and distances. For example, the quadratic equation can be used to find the area of a circle, the volume of a cylinder, or the distance between two points in three-dimensional space.

4. Solving optimization problems: The quadratic equation is used in optimization problems to find the maximum or minimum value of a function. For example, the quadratic equation can be used to find the maximum or minimum value of a parabolic arch, the optimal location for a satellite, or the best design for a bridge.

Overall, the quadratic equation is a powerful mathematical tool that has a wide range of uses in various fields of study. Its versatility and applicability make it an essential formula for anyone interested in solving problems related to motion, finance, geometry, and optimization.

Like Terms:

The secret is, just look at the variables (the letters) and their power. If the power and letters match, then it is a like term. The numerical coefficients can be negative or positive, and that's ok. Now let us check what the unlike terms look like. Please check the examples below.

Unlike Terms:

Just to remind you to focus on the term. It is separated by "+" and "-" signs. If one of them is mismatched with the other except the numerical then it is said it is an unlike term.

The FOIL Method in Factoring Quadratic Equation.

This is one way to familiarize the process of factoring quadratic equations, the FOIL method. Based on the picture above, the sequence was applied, e.i. First-Outside-Inside-Last for the sequence. Just go to this site for more explanation.

Illustrations:

Problem 1:

Given the two binomials to be multiplied below. We will use the illustration above to execute the sample.

Here, we must identify our First, Outside, Inside, and Last (FOIL) for the method. When we follow the sequence above (see the illustration), we found out that,

Take note that the middle term is the more-confusions sometimes because it varies depending on the preceding signs of the last terms of each binomial. Now, let us see the result with our second example below.

...and for the third example below.

Now, here's another example.

Problem 2:

A quadratic equation is given by: x^2 + 4x - 5 = 0

To solve this equation, we can use the quadratic formula, which is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this equation, a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

Using the quadratic formula, we can find the roots of the quadratic equation:

x = (-4 ± sqrt(4^2 - 4(1)(-5))) / 2(1)

Simplifying this expression, we get:

x = (-4 ± sqrt(44)) / 2

x = (-4 ± 2sqrt(11)) / 2

x = -2 ± sqrt(11)

Therefore, the solutions to the quadratic equation x^2 + 4x - 5 = 0 are:

x = -2 + sqrt(11) or x = -2 - sqrt(11)

The next sequence will be the series of samples.

Examples:

T's and a's were used in these examples but we can use all letters we want (even objects). This is just to show us how they, the two binomials, behaved when they were multiplied (distributed).

Now it's your turn. The author intentionally put an incomplete solution for you to work on. Let's start.

Complete what is missing in the equation.