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- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/08%3A_Analytic_Geometry/8.03%3A_The_ParabolaLike the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line...Like the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.
- https://math.libretexts.org/Courses/Las_Positas_College/Book%3A_College_Algebra/07%3A_Analytic_Geometry/7.02%3A_The_ParabolaLike the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line...Like the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.
- https://math.libretexts.org/Courses/Highline_College/MATH_141%3A_Precalculus_I_(2nd_Edition)/03%3A_Polynomial_and_Rational_Functions/3.02%3A_Quadratic_FunctionsIf the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. The vertex of the quadratic function is located at (h, k), where ...If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. The vertex of the quadratic function is located at (h, k), where h and k are the numbers in the transformation form of the function. The process for finding the x-intercepts is done commonly enough that sometimes people find it easier to solve the problem once in general and remember the formula for the result, rather than repeating the process each time.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/08%3A_Conic_Sections/8.01%3A_Distance_Midpoint_and_the_ParabolaA conic section is a curve obtained from the intersection of a right circular cone and a plane. The conic sections are the parabola, circle, ellipse, and hyperbola.
- https://math.libretexts.org/Courses/City_University_of_New_York/MAT1275_Basic/08%3A_Conics/8.01%3A_More_ParabolasTo graph a parabola that opens to the left or to the right is basically the same as what we did for parabolas that open up or down, with the reversal of the x and y variables. The graph is the...To graph a parabola that opens to the left or to the right is basically the same as what we did for parabolas that open up or down, with the reversal of the x and y variables. The graph is then the one we would get by graphing the equation with the x and y exchanged, and exchanging the x and y coordinates (e.g., if (2,3) is on the graph of the equation with the exchange, then (3,2) is on the graph of the given equation).
- https://math.libretexts.org/Workbench/MAT_2420_Calculus_II/07%3A_Parametric_Equations_and_Polar_Coordinates/7.06%3A_Conic_SectionsConic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection...Conic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection of a plane with a cone. If the plane is parallel to the axis of revolution (the y-axis), then the conic section is a hyperbola. If the plane is parallel to the generating line, the conic section is a parabola. If the plane is perpendicular to the axis of revolution, the conic section is a circle.
- https://math.libretexts.org/Courses/North_Hennepin_Community_College/Math_1120%3A_College_Algebra_(Lang)/04%3A_Conics/4.03%3A_Parabolas_and_Non-Linear_SystemsWhile we studied parabolas earlier when we explored quadratics, at the time we did not discuss them as a conic section. A parabola is the shape resulting from when a plane parallel to the side of the ...While we studied parabolas earlier when we explored quadratics, at the time we did not discuss them as a conic section. A parabola is the shape resulting from when a plane parallel to the side of the cone intersects the cone.
- https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/12%3A_Analytic_Geometry/12.04%3A_The_ParabolaLike the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line...Like the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/03%3A_Polynomial_and_Rational_Functions/3.03%3A_Quadratic_FunctionsIn this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. Working with quadratic functions can be less complex than working with h...In this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/11%3A_Parametric_Equations_and_Polar_Coordinates/11.05%3A_Conic_SectionsConic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection...Conic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection of a plane with a cone. If the plane is parallel to the axis of revolution (the y-axis), then the conic section is a hyperbola. If the plane is parallel to the generating line, the conic section is a parabola. If the plane is perpendicular to the axis of revolution, the conic section is a circle.
- https://math.libretexts.org/Courses/Coastline_College/Math_C115%3A_College_Algebra_(Tran)/08%3A_Analytic_Geometry/8.04%3A_The_ParabolaLike the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line...Like the ellipse and hyperbola, the parabola can also be defined by a set of points in the coordinate plane. A parabola is the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix.
