Completing the square for vertex form | Quadratic equations | Algebra I | Khan Academy | Summary and Q&A

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June 23, 2010
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Khan Academy
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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.

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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.

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