How To Convert From A Standard To A Vertex Form
Standard and vertex forms are mathematical equations used to describe the curve of a parabola. The vertex form can be thought of as a compressed parabolic equation, whereas the standard form is the longer, expanded version of the same equation. With a basic understanding of high school level algebra, you can convert the standard form to the vertex form.
Step 1
Start with the standard form of the parabolic equation; for example, y = (x + 3)² + 4. When plotted on a graph, the parabola will have a vertex of 3, 4.
Step 2
Expand the polynomial within the parentheses: (x+3)(x+3). Add the 4 back into the equation; you will now have (x+3)(x+3) + 4.
Step 3
Factor the polynomial. Start with the first X in the first parenthesis and multiply it by both the numbers in the second parenthesis: x² + 3x. Now take the 3 in the first parenthesis and multiply it by the numbers in the second: 3x + 9. Add the 4 into the equation so you have x² + 3x + 3x + 9 + 4.
Step 4
Combine like factors: x² has no like factor, so it stays as it is. There are two numbers with x, so add them as the equation states: 6x. Now add the 9 and the 4 so you have 13. Your final equation will be y = x² + 6x + 13.
TL;DR (Too Long; Didn't Read)
Show all of your work when solving equations.
Warning
Factoring the polynomials out of order will lead to the wrong results.
Cite This Article
MLA
Howell, Lindsay. "How To Convert From A Standard To A Vertex Form" sciencing.com, https://www.sciencing.com/convert-standard-vertex-form-7657147/. 24 April 2017.
APA
Howell, Lindsay. (2017, April 24). How To Convert From A Standard To A Vertex Form. sciencing.com. Retrieved from https://www.sciencing.com/convert-standard-vertex-form-7657147/
Chicago
Howell, Lindsay. How To Convert From A Standard To A Vertex Form last modified August 30, 2022. https://www.sciencing.com/convert-standard-vertex-form-7657147/