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Converting Quadratics: Standard Form and Vertex Form

Learn how to convert a quadratic between standard form (also called general form) and vertex form. Let's get started! 🚀

Converting Quadratics: Standard Form and Vertex Form - introduction visual

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Converting quadratic equations between general form y = ax² + bx + c and vertex form y = a(x - h)² + k, where a ≠ 0.Converting a quadratic equation from vertex form, y = 2(x - 3)² - 5, to general form by expanding and simplifying to y = 2x² - 12x + 13.Conversion of a quadratic equation from general form y = 3x² + 18x + 25 to vertex form by completing the square, resulting in y = 3(x + 3)² - 2.Converting the quadratic equation y = -2x² + 8x - 5 from general to vertex form using completing the square method, resulting in y = -2(x - 2)² + 3.

🛎️ What are Standard Form and Vertex Form?

  • Standard (general) form: y=ax2+bx+cy = ax^2 + bx + c
  • Vertex form: y=a(x−h)2+ky = a(x - h)^2 + k

🛎️ Converting Vertex Form to Standard Form

  • Expand the square using (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2, then expand the brackets
  • Don't forget the constant at the end (this is a very common mistake)

🛎️ Converting Standard Form to Vertex Form

  • Only factor out from the x2x^2 and xx terms. Ignore the constant
  • E.g. 3x2+18x→3(x2+6x)3x^2 + 18x \rightarrow 3(x^2 + 6x)

🛎️ Completing the Square

  • When completing the square, anything added inside must be undone outside
  • E.g. x2−4x=(x−2)2−22x^2 - 4x = (x - 2)^2 - 2^2

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