Graph the Parabola by Completing the Square and Using Focus and Vertex to Graph

Learn how to graph parabolas by first completing the square and transforming the equation into standard form! In this video, Mario's Math Tutoring will guide you through two examples, showing you how to identify the vertex, focus, and directrix, and understand whether the parabola opens up, down, left, or right. Master the process of converting general form equations into standard form to accurately sketch your parabolas. What you'll learn in this video: 0:00 - Introduction to graphing parabolas by completing the square 0:20 - Understanding the two standard forms of parabola equations (x² vs. y²) 0:40 - Example 1: Graphing y² + 12y + 2x + 8 = 0 1:00 - Rearranging terms to group 'y' variables 1:20 - Completing the square for the 'y' terms 1:50 - Factoring the perfect square trinomial 2:10 - Factoring out the leading coefficient on the 'x' terms 2:30 - Identifying the vertex (h, k) from standard form 2:50 - Determining the direction the parabola opens (left or right for y²) 3:00 - Calculating 'p' to find the focus and directrix 3:30 - Locating the focus and directrix on the graph 3:50 - Understanding the latus rectum (4p width at the focus) 4:10 - Example 2: Graphing x² + 6x + 5y + 19 = 0 4:30 - Rearranging terms to group 'x' variables 4:50 - Completing the square for the 'x' terms 5:10 - Factoring the perfect square trinomial 5:30 - Factoring out the leading coefficient on the 'y' terms 5:50 - Identifying the vertex (h, k) 6:10 - Determining the direction the parabola opens (up or down for x²) 6:20 - Calculating 'p' to find the focus and directrix 6:40 - Locating the focus and directrix 7:00 - Understanding the latus rectum width This tutorial is perfect for Precalculus students studying conic sections. Learn how to systematically convert parabola equations and accurately graph them with all key features! For more practice with completing the square and graphing parabolas, check out my other video right here! https://youtu.be/QD18uR-fIsg #Parabolas #CompletingTheSquare #ConicSections #Precalculus #GraphingParabolas #VertexFocusDirectrix #StandardForm #MathTutorial #MathHelp #MarioMathTutoring ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join