Completing the square for vertex form | Quadratic equations | Algebra I | Khan Academy

TL;DR

Learn how to write a quadratic equation in vertex form and identify the vertex of the parabola.

Transcript

Use completing the square to write the quadratic equation y is equal to negative 3x squared, plus 24x, minus 27 in vertex form, and then identify the vertex. So we'll see what vertex form is, but we essentially complete the square, and we generate the function, or we algebraically manipulate it so it's in the form y is equal to A times x minus B sq... Read More

Key Insights

• ❓ Divisible coefficients make it easier to manipulate quadratic equations.
• 🧑‍🏭 Factoring out a common factor simplifies equations for further manipulation.
• ❎ Completing the square allows for expressing part of the equation as a perfect square.
• 🔙 The vertex form of a quadratic equation is y = A(x - B)^2 + C, where (B, C) represents the vertex.
• 📈 For downward-opening graphs, A is negative; for upward-opening graphs, A is positive.
• 😑 Expressing an equation in vertex form helps determine the maximum or minimum value of a quadratic function.
• 😑 The x value of the vertex is the value that makes the expression inside the squared term equal to 0.

Questions & Answers

Q: What is the purpose of expressing a quadratic equation in vertex form?

Expressing a quadratic equation in vertex form helps identify the vertex of the parabola, which gives the minimum or maximum value of the function.

Q: How can we rewrite a quadratic equation in vertex form?

You can rewrite a quadratic equation in vertex form by completing the square and manipulating the equation algebraically to express part of it as a perfect square.

Q: How can we determine the x value of the vertex?

The x value of the vertex is the value that makes the expression inside the squared term equal to 0. In this case, it is the value of B.

Q: What does the y value of the vertex represent?

When the expression inside the squared term is equal to 0, the y value of the vertex is equal to C.

Summary & Key Takeaways

• The video teaches how to manipulate a quadratic equation to express it in the vertex form, y = A(x - B)^2 + C.

• Divisible coefficients make it easier to manipulate equations, and factoring out a common factor can help achieve this.

• By completing the square, it is possible to express part of the equation as a perfect square and simplify it further.