# Quadratic Formula Calculator

TLDRThis tutorial demonstrates how to use the quadratic formula calculator to solve equations of the form ax^2 + bx + c = 0. The example given is x^2 + 4x + 3 = 0, which yields solutions x = -1 and x = -3. The script explains the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), and guides viewers through identifying coefficients a, b, and c, then applying them to find the roots of the equation.

### Takeaways

- 🔢 The quadratic formula is used to solve equations in the form of ax^2 + bx + c = 0.
- 📘 The formula is expressed as x = (-b ± √(b^2 - 4ac)) / (2a).
- 🔍 In the example, the equation x^2 + 4x + 3 = 0 is solved using the quadratic formula.
- 📌 The values a, b, and c are identified from the equation: a = 1, b = 4, and c = 3.
- 🧮 The discriminant (b^2 - 4ac) is calculated to determine the nature of the roots.
- 📉 The discriminant for the example is 4^2 - 4*1*3, which simplifies to 16 - 12, resulting in 4.
- 📐 The square root of the discriminant (√4) is 2, indicating two real and distinct roots.
- 🔑 The two solutions for x are found by dividing the discriminant by 2a: (-4 + 2) / 2 and (-4 - 2) / 2.
- 📍 The solutions are x = -1 and x = -3, showcasing the two possible outcomes of the quadratic equation.
- 📝 The process is demonstrated both using a calculator and by hand calculation, emphasizing understanding and application.

### Q & A

### What is the purpose of the video?

-The purpose of the video is to demonstrate how to use the quadratic formula calculator to solve a quadratic equation.

### What is the quadratic equation used in the example?

-The quadratic equation used in the example is x^2 + 4x + 3 = 0.

### What are the values of 'a', 'b', and 'c' in the quadratic formula for the given equation?

-For the equation x^2 + 4x + 3 = 0, 'a' is 1, 'b' is 4, and 'c' is 3.

### How does the video demonstrate the use of the quadratic formula?

-The video demonstrates the use of the quadratic formula by plugging the values of 'a', 'b', and 'c' into the formula and solving for 'x'.

### What are the two possible solutions for 'x' in the example provided?

-The two possible solutions for 'x' are -1 and -3.

### What is the quadratic formula?

-The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the solutions for 'x' in a quadratic equation ax^2 + bx + c = 0.

### How does the video explain the process of solving the quadratic equation by hand?

-The video explains the process by identifying the coefficients 'a', 'b', and 'c', and then substituting these values into the quadratic formula to calculate the solutions.

### What is the significance of the plus-minus sign in the quadratic formula?

-The plus-minus sign in the quadratic formula indicates that there are two possible solutions for 'x', one using addition and the other using subtraction.

### What is the discriminant in the quadratic formula and how is it calculated?

-The discriminant is the expression under the square root (b^2 - 4ac) in the quadratic formula, which determines the nature of the roots of the quadratic equation.

### Why are there two answers for 'x' when using the quadratic formula?

-There are two answers for 'x' because the quadratic equation represents a parabola, which intersects the x-axis at two points, corresponding to the two solutions.

### How does the video ensure the viewer understands the quadratic formula?

-The video ensures understanding by providing a step-by-step walkthrough of the formula's application, from identifying coefficients to calculating the discriminant and solving for 'x'.

### Outlines

### 🔢 Introduction to Using the Quadratic Formula Calculator

The video begins by welcoming viewers and introduces the quadratic formula calculator. It explains how to solve a quadratic equation, such as x^2 + 4x + 3 = 0, by entering it into the calculator. Upon hitting enter, the calculator provides the solutions: x = -1 or x = -3. The presenter then states the intention to explain the steps manually, demonstrating the use of the quadratic formula.

### 📝 Explanation of the Quadratic Formula

The presenter explains the quadratic formula, which can be used to solve equations of the form ax^2 + bx + c = 0. The formula is presented as X = (-B ± √(B^2 - 4AC)) / (2A). The next step involves identifying the coefficients 'A', 'B', and 'C' from the equation. For the example equation x^2 + 4x + 3 = 0, 'A' is 1, 'B' is 4, and 'C' is 3. These values are then plugged into the formula to compute the solutions.

### 🧮 Calculating Step-by-Step Using the Formula

The presenter demonstrates the step-by-step process of plugging the coefficients into the quadratic formula. First, 'B' is substituted as -4, and the expression under the square root (B^2 - 4AC) is calculated. After evaluating B^2 as 16 and 4AC as 12, the result is 4 under the square root, which equals 2. The final step calculates the two possible values for X: -4 + 2 / 2 = -1 and -4 - 2 / 2 = -3. The solutions are confirmed as -1 and -3.

### Mindmap

### Keywords

### 💡Quadratic Formula

### 💡Quadratic Equation

### 💡Coefficients

### 💡Square Root

### 💡Discriminant

### 💡Plus or Minus

### 💡Calculator

### 💡Algebra

### 💡Solving Equations

### 💡Roots

### Highlights

Introduction to the Quadratic Formula Calculator

Demonstration of solving x^2 + 4x + 3 = 0 using the calculator

Calculator output showing two solutions: x = -1 or x = -3

Explanation of the quadratic formula

Quadratic formula presented: x = (-b ± √(b^2 - 4ac)) / (2a)

Identification of coefficients a, b, and c in the equation

Step-by-step substitution of a, b, and c into the quadratic formula

Calculation of the discriminant (b^2 - 4ac)

Solution for x when using the plus sign in the quadratic formula

Solution for x when using the minus sign in the quadratic formula

Final solutions for x: -1 and -3

Emphasis on the importance of the discriminant in determining the number of solutions

Practical application of the quadratic formula in solving real-world problems

Visual demonstration of the calculator's process for solving quadratic equations

Tutorial on how to input a quadratic equation into the calculator

Clarification of the quadratic formula's components and their significance