Find the Equation of a Parabola Given Vertex, Axis of Symmetry and a Point

Learn how to write the equation of a parabola when you're given its vertex, the orientation of its axis of symmetry (vertical or horizontal), and another point it passes through! This video breaks down the key concepts and formulas, guiding you through two detailed examples to help you master this important skill in pre-calculus and algebra 2. In this tutorial, you will discover: What is a Parabola? A quick review of the definition (equidistant from focus and directrix) and key components like the vertex, focus, and directrix. Two Forms of Parabola Equations: x² form: For parabolas opening up or down (vertical axis of symmetry). y² form: For parabolas opening right or left (horizontal axis of symmetry). Understanding the Axis of Symmetry: How knowing if the axis is vertical or horizontal tells you which equation form to use. The Role of 'p' (Focal Distance): What p represents (distance from vertex to focus or vertex to directrix) and how 4p appears in the standard equations. Step-by-Step Process: Step 1: Choose the Correct Equation Form: Based on the axis of symmetry (vertical or horizontal). Step 2: Substitute the Vertex (h, k): Plug the coordinates of the vertex into the chosen equation. Step 3: Substitute the Given Point (x, y): Use the coordinates of the additional point on the parabola. Step 4: Solve for 4p: Perform algebraic steps to isolate the 4p term. Step 5: Write the Final Equation: Substitute the value of 4p back into the equation along with your h and k values. Bonus: Finding the Focus and Directrix: Briefly learn how to use the calculated p value to locate the focus and directrix of the parabola. Example 1: Vertical axis of symmetry, vertex at (2, 3), passing through (3, -1). Example 2: Horizontal axis of symmetry, vertex at (-2, -4), passing through (2, -2). This video is perfect for algebra 2 and pre-calculus students learning about conic sections and writing parabola equations! Timestamps: 0:00 - Introduction to Writing Parabola Equations 0:20 - What is a Parabola? (Focus, Directrix, Vertex) 0:50 - Two Forms of Parabola Equations (x² vs. y²) 1:20 - Example 1: Vertical Axis of Symmetry, Vertex (2, 3), Point (3, -1) 1:50 - Choosing the Correct Equation Form 2:10 - Substituting the Vertex (h, k) 2:40 - Understanding p (Focal Distance) 3:00 - Substituting the Given Point (x, y) and Solving for 4p 3:40 - Writing the Final Equation 4:00 - Bonus: Finding the Focus and Directrix for Example 1 4:40 - Example 2: Horizontal Axis of Symmetry, Vertex (-2, -4), Point (2, -2) 5:00 - Choosing the Correct Equation Form 5:20 - Substituting the Vertex (h, k) 5:50 - Substituting the Given Point (x, y) and Solving for 4p 6:30 - Writing the Final Equation 6:50 - Bonus: Finding the Focus and Directrix for Example 2 7:20 - Conclusion & More Parabola Practice Don't forget to like, comment, and subscribe for more algebra and pre-calculus tutorials! #ParabolaEquation #ConicSections #VertexForm #AxisOfSymmetry #Algebra2 #PreCalculus #MathTutorial #GraphingParabolas ➡️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