Graphing parabola using methods of squares word
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This document provides steps for graphing a parabola using the method of squares. It explains that you draw six squares with sides equal to four times the focus of the parabola. It then outlines the steps to transform the equation into the standard form to locate the vertex and focus. As an example, it shows how to graph the parabola with the equation x^2 = 12y by transforming it into standard form and using the focus at (0,3) to draw six 3x3 squares and locate the points on the parabola.
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ito ang gabay ng mga guro na nagturo ng values education sa public school sa pilipinas dep ed nakakatulong ito sa atin
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Graphing parabola presentation
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. Samples are worked through, showing how to identify the focus, directrix, vertex and ordered point pairs on the parabola by placing squares along these key points and locations.
Graphing parabola presentation
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 x2=6y and y2=8x. The focus, vertex, directrix, and latus rectum are identified for each parabola by comparing the equations to the standard forms x2=4py and y2=4px.
Graphing parabola presentation
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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1. The document discusses parabolas and their key characteristics including focus, directrix, and standard equation forms.
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3. The standard equation forms for parabolas are provided depending on the orientation and location of the vertex.
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This document provides an overview of parabolas including their key characteristics and equations. It defines a parabola as the set of all points that are an equal distance from both a fixed point called the focus and a fixed line called the directrix. The standard equation of a parabola is provided and examples are given of writing the equation of a parabola given its focus and directrix. The document also discusses graphing parabolas by identifying the vertex, axis of symmetry, focus, and directrix. Real-world applications of parabolas to reflect light and sound are briefly described.
introduction to conics: parabola
1. The document provides information about an upcoming lecture and test on conic sections, specifically parabolas.
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3. Examples are given of finding the equation of a parabola given its geometric properties, and finding the focus and directrix of a parabola given its equation. Applications of parabolas as reflectors are also mentioned.
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The document discusses parabolas, including their key properties and equations. It defines a parabola as the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix). The document derives the standard equation of a parabola from this definition and discusses how to graph parabolas based on their equations. It also covers transformations, latus rectum, and other geometric properties of parabolas.
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Identify the vertex, directrix, focus, and axis of a parabola.
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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
parabolas
The document discusses parabolas and their key properties. It begins by introducing the standard form of a quadratic function and the steps to find the vertex, line of symmetry, and maximum/minimum value. It then provides examples of completing the square to derive the standard form (y = (x - h)2 + k) from other forms. Using this standard form, the vertex is identified as (h, k), the line of symmetry is defined as x = h, and the maximum/minimum is determined by the sign of the parabola based on whether k represents the highest or lowest point.
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
Lecture 2b Parabolas.pdf
This document provides an overview of parabolas including:
(1) The definition of a parabola as the locus of points equidistant from a fixed point (the focus) and fixed line (the directrix)
(2) The key parts of a parabola including the vertex, axis of symmetry, focus, directrix, and latus rectum
(3) How to write the standard and general forms of the equation of a parabola and how to convert between the two forms
(4) The steps to graph a parabola given its equation in vertex form
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.
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The document provides instruction on completing the square, a method for solving quadratic equations that are not factorable. It explains the five steps: 1) divide by the leading coefficient, 2) rewrite in the form ax + by = c, 3) find half of b and square it, adding it to both sides, 4) rewrite the perfect square trinomial and take the square root of both sides, and 5) solve for x. An example is worked through applying these steps to solve the equation x^2 - 16x + 15 = 0. The document also reviews graphing quadratic functions and finding solutions, axis of symmetry, vertex and y-intercepts.
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The document defines and discusses parabolas. A parabola is the set of all points equidistant from a fixed point called the focus and a line called the directrix. The key parts of a parabola are identified as the vertex, focus, directrix, axis of symmetry, and latus rectum. An algebraic definition and process for graphing a parabola given its equation is provided. An example parabola with the equation (x - 5)2 = 12(y – 6) is graphed step-by-step as an illustration.
Chapters Summary (X class)
Extra-Questions, Pics & Summary available and easy way to find square roots & cube roots available.......ENJOY....!!!!!!!
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Graphing parabola using methods of squares word
- 1. Graphing parabola using methods of squares What you need to do is that you just draw six squares with sides four times the focus then you can visualize the graph of a parabola provided you already locate the vertex of the parabola. Here are the steps you will follow: Translate the equation to form x2= 4py for the parabola with vertex at the origin. And (x-h)2= 4p(y-k) for the parabola with vertex at (h,k)
- 2. Sample : Plot the graph of x2 = 12y. Solution: transform the equation to x2 =4py 4py=12y : if we divide both sides by 4y we will get p= 3 With these data we can now graph the parabola in which our the focus is at (0,p) or (0,3), the directrix is y=-p or y=-3. What we need is now to construct the six squares with sides 2p or 6 units
- 3. The line in violet is the length of latus rectum, while the left-right arrow in blue is the directrix, and the circles in red are the ordered pairs of the parabola foud at the edges of the squares.
- 4. Thank you for viewing Virgilio rollon paragele Teacher at Tomas cabili national high school