Judes Drafting Table The Bowling Question
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The document describes a bowling pin arrangement that forms a parabola. It provides information about the vertex, focus point, and rows of pins. Lucy asks the narrator to write the equation of the parabola and determine if the point (4,5) lies on it. The narrator analyzes the information given about the parabola's standard form and properties to derive the equation and verify the point.
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Slavery Module: Lesson thirteen
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Parabola complete
This summary combines slides from Melanie Tomlinson and Morrobea on the topic of parabolas. The key points covered include:
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Math1.2
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.
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Logic.pdf
Logic is the science of correct thinking. Aristotle is considered the father of logic. A proposition is a statement that is either true or false. George Boole developed symbolic logic using symbols like conjunction, disjunction and negation. Truth tables show the truth values of compound propositions based on the truth values of simple statements. Magic squares are grids filled with numbers where the sums of each row, column and diagonal are equal. There are methods for constructing magic squares of various sizes like 3x3, 4x4 and 5x5.
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5.2 solve quadratic equations by graphing.vertex and intercept form
Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
= 3x^2 + 12x + 12 - 4
= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where: a = 3
h = 0
k = 8
So the equation in vertex form is:
y = 3(x - 0)^2 + 8
Or simply:
y = 3x^2 + 8
4.2 vertex and intercept form
Okay, let's solve this step-by-step:
1) FOIL the expression: y = 3(x + 2)(x + 2) - 4
= 3(x^2 + 4x + 2x + 4) - 4
= 3x^2 + 12x + 12 - 4
= 3x^2 + 12x + 8
2) This is in the vertex form: y = a(x - h)^2 + k
Where:
a = 3
h = -2
k = 8
So the equation in vertex form is:
y = 3(x - (-2))^2 + 8
y = 3(x + 2)^2 - 4
Quadratic function
The document discusses quadratic functions and their zeros. It provides examples of finding the zeros of quadratic functions by factoring, completing the square, and using the quadratic formula. It also gives examples of writing the equation of a quadratic function given its zeros or given properties like the vertex and y-intercept. Methods discussed include using the fact that the zeros are the roots of the corresponding equation, and substituting known point values into the quadratic formula.
9.2 - parabolas 1.ppt discussion about parabola
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
Solving Quadratics by Graphing
This document discusses solving quadratic equations by graphing. It defines the terms of a quadratic equation and explains that the solutions are the x-intercepts where the graph crosses the x-axis. A quadratic equation will have 0, 1, or 2 real solutions. The graph of a quadratic equation is a parabola with an axis of symmetry. The vertex is the maximum or minimum point, and it can be found using the formula. Graphing involves finding the axis of symmetry, vertex, and using a table to plot additional points to draw the smooth curve.
parabola class 12
This document discusses parabolas, including their key features like the vertex, focus, directrix, and axis of symmetry. It provides examples of how to graph parabolas given their standard form equations, both for parabolas with vertices at the origin and for parabolas with other vertices. It also shows how to write the standard form equation of a parabola when given its focus and directrix.
4.2 vertex and intercept form
This document discusses graphing quadratic functions in vertex and intercept forms. It defines key terms like vertex, axis of symmetry, and parabola. It explains how to graph quadratic functions written in vertex form and intercept form. Examples are provided for graphing functions in each form. The document also discusses how to change between the vertex, intercept, and standard forms of a quadratic equation.
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5.2 solve quadratic equations by graphing.vertex and intercept form
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- 4. .:. THE DIAGRAM .:. CARPET WOODEN FLOOR FOCUS POINT (0, 8) VERTEX (h, k) parabola y x p = 4
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