Quadratic Formula Calculator

MathPapa
16 Feb 201703:10

TLDRThis video demonstrates how to use a quadratic formula calculator to solve equations like x^2 + 4x + 3 = 0. The solution is calculated as x = -1 or x = -3. The video walks through the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / 2a. It explains how to identify the values of a, b, and c from the equation and shows step-by-step how to substitute these values into the formula. By breaking down the process, it simplifies solving quadratic equations by hand and using a calculator.

Takeaways

  • 📐 The video is about using a quadratic formula calculator.
  • 🧮 The example given is solving the equation x^2 + 4x + 3 = 0.
  • 💻 The speaker inputs the equation into the calculator, and the solution provided is x = -1 or x = -3.
  • 🔢 The quadratic formula is explained as x = (-b ± √(b² - 4ac)) / 2a.
  • 🅰️ The coefficients in the equation are identified as a = 1, b = 4, and c = 3.
  • 📊 These values are plugged into the quadratic formula for solving.
  • 🧠 The discriminant (b² - 4ac) is calculated: 16 - 12 = 4.
  • ✔️ The square root of 4 is 2, leading to two possible solutions.
  • ➕ The first solution is x = (-4 + 2) / 2, which simplifies to x = -1.
  • ➖ The second solution is x = (-4 - 2) / 2, which simplifies to x = -3.

Q & A

  • What equation is solved in the video?

    -The equation solved is x^2 + 4x + 3 = 0.

  • How does the quadratic formula solve for x?

    -The quadratic formula is x = (-B ± √(B^2 - 4AC)) / 2A.

  • What are the values of A, B, and C for the equation x^2 + 4x + 3 = 0?

    -A = 1, B = 4, and C = 3.

  • What is B^2 - 4AC in this case?

    -B^2 - 4AC = 16 - 12 = 4.

  • What is the square root of B^2 - 4AC?

    -The square root of 4 is 2.

  • How is the first solution for x calculated?

    -The first solution is x = (-4 + 2) / 2, which simplifies to x = -1.

  • How is the second solution for x calculated?

    -The second solution is x = (-4 - 2) / 2, which simplifies to x = -3.

  • What does the calculator provide as the solutions?

    -The calculator provides x = -1 or x = -3.

  • Why are there two possible solutions for x?

    -There are two solutions because of the ± in the quadratic formula, leading to a positive and a negative result.

  • What is the purpose of the video?

    -The purpose of the video is to explain how to use a quadratic formula calculator and walk through solving a quadratic equation by hand.

Outlines

00:00

📐 Introduction to Using the Quadratic Formula Calculator

This paragraph introduces the video tutorial on using a quadratic formula calculator. It starts with the problem x² + 4x + 3 = 0, showing how to input the equation into the calculator to obtain the result. The calculator determines that the solution is x = -1 or x = -3. The presenter then hints at explaining the manual steps for solving the equation using the quadratic formula.

✏️ Understanding the Quadratic Formula and Variable Identification

This paragraph explains the quadratic formula and how it applies to equations of the form ax² + bx + c = 0. The formula is given as x = [-b ± √(b² - 4ac)] / 2a. The presenter identifies the values of a, b, and c from the equation x² + 4x + 3 = 0. Specifically, a is the coefficient of x² (which is 1), b is the coefficient of x (4), and c is the constant (3).

🔍 Applying the Quadratic Formula with a = 1, b = 4, and c = 3

Here, the presenter plugs the values of a, b, and c into the quadratic formula. The calculation follows: x = [-4 ± √(4² - 4(1)(3))] / 2(1). The value under the square root (the discriminant) is 16 - 12, which simplifies to √4. Therefore, the square root of 4 is 2, leaving two possible solutions for x, based on adding or subtracting the square root.

✅ Finding the Two Solutions for x

In this final part, the presenter computes the two possible solutions for x. First, x = (-4 + 2) / 2, which simplifies to x = -1. Then, x = (-4 - 2) / 2, which gives x = -3. The two solutions are therefore x = -1 or x = -3, matching the result from the calculator. The step-by-step process concludes with the two answers verified manually.

Mindmap

Keywords

💡Quadratic Formula

The quadratic formula is a solution to quadratic equations of the form ax^2 + bx + c = 0. It is represented as x = [-b ± sqrt(b^2 - 4ac)] / 2a. The formula provides the solutions (roots) for x and is used in the video to solve a specific equation, demonstrating how to calculate both the positive and negative roots.

💡Equation

An equation is a mathematical statement that asserts the equality of two expressions. In the video, the specific equation being solved is x^2 + 4x + 3 = 0, which is a quadratic equation. The goal is to solve for the variable x using the quadratic formula.

💡Coefficients

Coefficients are the numerical factors in front of variables in an equation. In the video, 'a', 'b', and 'c' are the coefficients for the terms involving x^2, x, and the constant, respectively. For the equation x^2 + 4x + 3 = 0, a = 1, b = 4, and c = 3.

💡Discriminant

The discriminant is the part of the quadratic formula under the square root, represented as b^2 - 4ac. It determines the nature of the roots of the equation. In the video, the discriminant is calculated as 16 - 12 = 4, which results in real and distinct roots for the equation.

💡Roots

Roots are the solutions to the equation when set equal to zero. In the video, after applying the quadratic formula, the roots for the equation x^2 + 4x + 3 = 0 are determined to be x = -1 and x = -3, which are the points where the equation equals zero.

💡Square Root

The square root is a mathematical function that, when applied to a number, returns a value that, when multiplied by itself, equals the original number. In the video, the square root of 4 (√4) is computed as part of the quadratic formula, yielding the value 2.

💡Plus or Minus (±)

The ± symbol represents two possible outcomes in the quadratic formula: one involving addition and the other involving subtraction. This symbol indicates that the equation has two possible solutions, which is demonstrated in the video when calculating x = -1 and x = -3.

💡Variable

A variable is a symbol used to represent an unknown value in an equation. In this video, 'x' is the variable whose value is being solved for using the quadratic formula. The video explains how to find the values of x that satisfy the given equation.

💡Constant

A constant is a fixed value that does not change. In the equation x^2 + 4x + 3 = 0, the number 3 is the constant term, represented by 'c' in the quadratic formula. It is part of the equation but does not depend on the variable x.

💡Solution

The solution to an equation is the value of the variable that satisfies the equation. In the video, the solutions to the quadratic equation x^2 + 4x + 3 = 0 are x = -1 and x = -3, which are obtained by applying the quadratic formula step by step.

Highlights

Welcome and introduction to using the quadratic formula calculator.

Example problem: Solving x^2 + 4x + 3 = 0 using the calculator.

Typing the equation into the calculator and obtaining the result.

Calculator computes the solution: x = -1 or x = -3.

Explanation of solving the quadratic equation by hand.

Quadratic formula introduction: x = (-B ± sqrt(B^2 - 4AC)) / 2A.

Identifying coefficients A, B, and C from the equation.

Plugging the coefficients into the quadratic formula.

Detailed calculation under the square root: B^2 - 4AC.

Simplification of the expression under the square root.

Calculating the square root value.

Deriving two potential solutions from the quadratic formula.

Calculation of the first solution: x = -1.

Calculation of the second solution: x = -3.

Summary of solving quadratic equations both by calculator and manually.

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