Graphing parabola presentation
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This document discusses graphing parabolas using squares. It explains that parabolas can be graphed by comparing their equations to standard forms and using squares of length 2p, where p is determined by the equation. Examples are given of graphing parabolas from equations x^2=6y and y^2=8x. The focus, vertex, directrix, and latus rectum are identified for each parabola by comparing the equations to the standard forms.
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1576 parabola
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Parabola complete
This summary combines slides from Melanie Tomlinson and Morrobea on the topic of parabolas. The key points covered include:
- The geometric definition of a parabola as the set of all points equidistant from a fixed point (the focus) and fixed line (the directrix).
- Parabolas can be represented using various equation forms including vertex form, standard form, and general form.
- Methods for graphing parabolas by identifying features like the vertex, axis of symmetry, x-intercepts, focus, and directrix.
- Applications of parabolas to model real-world situations like searchlights and radio telescopes.
Parabola
The document defines a parabola geometrically as the set of all points in a plane that are the same distance from a fixed point, called the focus, as they are from a fixed line, called the directrix. It provides examples of parabolas in standard form with the vertex at various points and opening in different directions. It also discusses how to write the standard form equation of a parabola given its focus and vertex, as well as how to find the focus and directrix of a parabola given its equation. Finally, it demonstrates how to use the method of completing the square to convert a general quadratic equation into the standard form needed for graphing a parabola.
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1. The document discusses parabolas and their key characteristics including focus, directrix, and standard equation forms.
2. A parabola is defined as the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
3. The standard equation forms for parabolas are provided depending on the orientation and location of the vertex.
Parabola
The document discusses parabolas and their key properties:
- A parabola is defined as the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
- The vertex is the point where the axis of symmetry intersects the parabola. The focus and directrix are a fixed distance (p) from the vertex.
- The latus rectum is the line segment from the focus to the parabola, perpendicular to the axis of symmetry. Its length is determined by the equation of the parabola.
Finding the Focus & Directrix of a Parabola
This document discusses parabolas and how to find their focus and directrix. A parabola is defined as the set of points equally distant from a fixed line and point not on the line. The document provides formulas for finding the focus and directrix of parabolas with their vertex at (0,0) or at a point (h,k). It emphasizes that the x-coordinate of the focus corresponds to p if x is squared in the formula, and the y-coordinate of the focus corresponds to p if y is squared.
Notes parabolas
The document discusses the properties of parabolas that open up or down and parabolas that open left or right. It provides the general form and standard form of each, noting that a positive value of a in the standard form indicates the direction the parabola opens (up if discussing vertical parabolas, right if discussing horizontal parabolas) while a negative a indicates the opposite direction. It also identifies the axis of symmetry formula for each. Examples are given to demonstrate finding the direction a parabola opens, its vertex, and axis of symmetry.
Properties of Parabola
This document discusses properties of parabolas including:
- The relationship between the focus and directrix of a parabola and any point on the parabola.
- The standard form equations of parabolas depending on their orientation and location of the vertex.
- Converting between standard, general, and vertex forms of parabolic equations.
- Examples of determining the vertex, focus, directrix, and axis of symmetry from equations and vice versa.
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1576 parabola
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Parabola complete
This summary combines slides from Melanie Tomlinson and Morrobea on the topic of parabolas. The key points covered include:
- The geometric definition of a parabola as the set of all points equidistant from a fixed point (the focus) and fixed line (the directrix).
- Parabolas can be represented using various equation forms including vertex form, standard form, and general form.
- Methods for graphing parabolas by identifying features like the vertex, axis of symmetry, x-intercepts, focus, and directrix.
- Applications of parabolas to model real-world situations like searchlights and radio telescopes.
Parabola
The document defines a parabola geometrically as the set of all points in a plane that are the same distance from a fixed point, called the focus, as they are from a fixed line, called the directrix. It provides examples of parabolas in standard form with the vertex at various points and opening in different directions. It also discusses how to write the standard form equation of a parabola given its focus and vertex, as well as how to find the focus and directrix of a parabola given its equation. Finally, it demonstrates how to use the method of completing the square to convert a general quadratic equation into the standard form needed for graphing a parabola.
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1. The document discusses parabolas and their key characteristics including focus, directrix, and standard equation forms.
2. A parabola is defined as the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
3. The standard equation forms for parabolas are provided depending on the orientation and location of the vertex.
Parabola
The document discusses parabolas and their key properties:
- A parabola is defined as the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
- The vertex is the point where the axis of symmetry intersects the parabola. The focus and directrix are a fixed distance (p) from the vertex.
- The latus rectum is the line segment from the focus to the parabola, perpendicular to the axis of symmetry. Its length is determined by the equation of the parabola.
Finding the Focus & Directrix of a Parabola
This document discusses parabolas and how to find their focus and directrix. A parabola is defined as the set of points equally distant from a fixed line and point not on the line. The document provides formulas for finding the focus and directrix of parabolas with their vertex at (0,0) or at a point (h,k). It emphasizes that the x-coordinate of the focus corresponds to p if x is squared in the formula, and the y-coordinate of the focus corresponds to p if y is squared.
Notes parabolas
The document discusses the properties of parabolas that open up or down and parabolas that open left or right. It provides the general form and standard form of each, noting that a positive value of a in the standard form indicates the direction the parabola opens (up if discussing vertical parabolas, right if discussing horizontal parabolas) while a negative a indicates the opposite direction. It also identifies the axis of symmetry formula for each. Examples are given to demonstrate finding the direction a parabola opens, its vertex, and axis of symmetry.
Properties of Parabola
This document discusses properties of parabolas including:
- The relationship between the focus and directrix of a parabola and any point on the parabola.
- The standard form equations of parabolas depending on their orientation and location of the vertex.
- Converting between standard, general, and vertex forms of parabolic equations.
- Examples of determining the vertex, focus, directrix, and axis of symmetry from equations and vice versa.
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This document defines and discusses parabolas. It begins by listing 4 learning outcomes related to understanding parabolas, their standard form equations, graphing them, and solving problems involving parabolas. It then defines a parabola as the set of all points that are the same distance from both a fixed focus point and directrix line. The standard form of the equation for a parabola is derived and explained to be x^2 = 4cy, where c is the distance between the focus and directrix. Key features of parabolas like the vertex, directrix, focus, and axis of symmetry are identified. Examples of determining standard equations and graphing parabolas are provided.
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Watch this presentation to find out.
Here, we learn how a parabola is derived when a plane cuts a cone. We learn that, for a parabola, distance of a point from the focus = distance of the point from the directrix. We solve problems based on this principle and also learn how to calculate equation of the axis and the coordinates of the vertex.
This is useful for grade 11 maths students. This channel has videos for grades 11, 12, engineering maths, nata maths and the GRE QUANT section.
Consider subscribing to my channel for more videos. You can visit my page
https://www.mathmadeeasy.co/lessons
For further help, you can join my classes for grade 11 maths
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For further help, you can join my classes for grade 11 maths
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The document discusses parabolas including their parts, graphs, and equations. It defines a parabola as the locus of points where the distance to the focus is equal to the distance to the directrix. The parts of a parabola include the vertex, focus, directrix, axis of symmetry, and latus rectum. The document outlines the graphs of parabolas with the vertex at the origin or at a point (h,k), and opening in different directions. It notes equations will be provided for parabolas with the vertex at the origin or (h,k), but does not show the actual equations.
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In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y=ax²+bx+c is a parabola if a≠0, and, conversely, a parabola is the graph of a quadratic function if its axis is parallel to the y-axis. The line perpendicular to the In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y=ax²+bx+c is a parabola if a≠0, and, conversely, a parabola is the graph of a quadratic function if its axis is parallel to the y-axis. The line perpendicular to the In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y=ax²+bx+c is a parabola if a≠0, and, conversely, a parabola is the graph of a quadratic function if its axis is parallel to the y-axis. The line perpendicular to the In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line. The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic s
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22 the graphs of quadratic equations
The document discusses how to graph quadratic equations by plotting parabolas. It provides examples of graphing the equations y = -x^2 and y = x^2 - 4x - 12. It explains that the graphs of quadratic equations form parabolas with properties including symmetry around the vertex. The vertex formula is provided. Methods for graphing parabolas include making a table around the vertex or finding the vertex, another point like the y-intercept, and the reflection of that point.
6. 1 graphing quadratics
The document discusses graphing quadratic functions. It defines a quadratic function as an equation of the form y=ax^2 +bx+c where a ≠ 0, forming a U-shaped parabola. It explains that the vertex is the highest/lowest point and the axis of symmetry is the vertical line through the vertex. It provides steps for graphing a quadratic function by finding the vertex coordinates using the standard form equation, choosing x-values on each side of the vertex, calculating corresponding y-values, and plotting points connected with a smooth curve. An example problem demonstrates these steps.
Unit 8.1
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10.1 Parabolas
Identify the vertex, directrix, focus, and axis of a parabola.
Write the equation of a parabola in vertex form.
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Oct 19 And 20 Notes Quadratics roots and substitution
These documents discuss solving quadratic equations by rewriting them in standard form and using substitution. Key steps include temporarily substituting a variable like p for x^2 to transform the equation, then solving the resulting quadratic for p and back-substituting to find the solutions for x. The roots of a quadratic equation can be used to find the vertex and axis of symmetry of the parabola using the formula that the x-coordinate of the vertex equals the average of the roots. Additionally, if the roots are known, the quadratic equation can be generated by using the formula that the coefficient of the x-term equals the sum of the roots and the constant term equals the product of the roots.
2.8.5 Coordinate Plane Quads
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Transformaciones de Coordenadas
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- Examples of transforming points between rectangular and polar coordinates.
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Notes 3-4
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Conic sections- Parabola STEM TEACH
The document provides the steps to write the equation of a parabola in standard form given certain information about its properties. It then works through two example problems:
1) Given the equation of a parabola in general form, it rewrites the equation in standard form and determines the vertex, focus, directrix, and axis of symmetry.
2) Given the vertex and directrix of a parabola, it derives the standard form equation that satisfies those conditions.
3) Given the height and base width of an arch with a parabolic shape, it illustrates the situation, determines the necessary values, and writes the standard form equation that models the arch's shape.
6.4 intercept form
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We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
Taking AI to the Next Level in Manufacturing.pdf
Read Taking AI to the Next Level in Manufacturing to gain insights on AI adoption in the manufacturing industry, such as:
1. How quickly AI is being implemented in manufacturing.
2. Which barriers stand in the way of AI adoption.
3. How data quality and governance form the backbone of AI.
4. Organizational processes and structures that may inhibit effective AI adoption.
6. Ideas and approaches to help build your organization's AI strategy.
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Graphing parabola presentation
- 1. Using the method of squares
- 2. The parabola we are to graph are having origin as our vertex
- 3. Compare the equation to x2=4py for a parabola with y-axis as its axis of symmetry
- 4. Compare the equation to y2=4px for a parabola with x-axis as its axis of symmetry
- 5. In graphing parabola we use squares to asses our graphing
- 6. Parts of a parabola Focus: F(0,p) for a parabola of the form x2=4py
- 7. Use the six squares whose sides equal to 2p
- 8. Sample: x2=6y Solution: compare the problem , x2 =6y to x2 = 4py 4py=6y by transitive property, and p=1.5 by dividing 4y to both sides
- 9. From the results Focus (0, 1.5) or (0,p) Length of latus rectum 4p or 6 units Vertex (0,0) Directrix: y= -1.5 or y= -p
- 10. We draw the graph using six squares with sides equal to 2p or 3 units
- 11. x2 =6y length of latus rectum 6 1 2 5 4 3 Vertex (0,0) Directrix: y= -1.5
- 12. The ordered pairs The red colors on previous slide are the points on the parabola. The ordered pairs are found on the vertex of the squares, upper vertex of squares 1,3,4 and 6. The lower portion which is the origin is found on the sides of squares 3 and 4.
- 13. Sample 2: y2 =8x In this case the graph has an axis of symmetry which is the x- axis , and the directrix is at the left side of the origin
- 14. Solution y2= 8x will be compared to y2=4px, which yields p=2
- 15. The squares Length of latus rectum directrix Vertex (0,0) The red colored are the points on the parabola that passes the edges of the squares All the squares have the sides of 4 units
- 16. Thank you for viewing
- 17. Virgilio Rollon Paragele Tomas Cabili National High School