define parabola
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Parabola Definition of Parabola. A parabola is the set of all points in a plane that are equidistant from the focus and the directrix of the parabola. The graph of any quadratic equation is a parabola.
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Equation of a Parabola The vertex form of a parabola's equation is generally expressed as: y = a(x-h)2+k. ( 1 h,k) is the vertex as you can see in the picture below.  If a is positive then the parabola opens upwards like a regular U.
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Ellipse This ratio is called the eccentricity, and for a hyperbola it is always greater than 1. The hyperbola is an open curve (has no ends). But that isn't the full story! Because a hyperbola is actually two separate curves in mirror image like this: On the diagram you can see: 1  a directrix and a focus (one on each side)  an axis of symmetry (that goes through each focus, at right angles to the directrix)
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parabola Definition of parabola for English Language Learners. : a curve that is shaped like the path of something that is thrown forward and high in the air and falls back to the ground.
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Eccentricity of an Orbit A parabola has an eccentricity of exactly one, while hyperbolas have eccentricities greater than one. Parabolic and hyperbolic trajectories are not orbits; they only result in a single close pass by the parent body, while orbits result in repeated close approaches.
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- Parametric Equations and the Parabola (Extension 1) Parametric Equations. • Parametric equations are a set of equations in terms of a parameter that represent a relation. • Each value of the parameter, when evaluated in the parametric equations, corresponds to a point. along the curve of the relation.
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What Is the Variable Plotted on the Horizontal, or X-Axis, Called? The variable plotted on the horizontal, or X-axis, is called the predictor, independent or explanatory variable. the variable plotted on the vertical, or Y-axis, is called the dependent or response variable. These terms are often used in graphs plotting the results of correlation analyses and linear regression. Continue Reading.
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- The definition of a parabola is the set of all points that are equidistant to a focal point and a line called a directrix. Howver, it is best recognized by its classic u-shape. Parabolas either open up, down, right, or left.
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- If you graph a linear function, you get a line. If you graph a quadratic function, you get something called a parabola. A parabola tends to look like a smile or a frown, depending on the function. Check out this tutorial and learn about parabolas!
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- The graphical representation of quadratic equations are based on the graph of a parabola. A parabola is an equation of the form y = a x 2 + bx + c. The most general parabola, shown at the right, has the equation y = x 2. The coefficent, a, before the x 2. The vertex 2, the vertex is (0,0).
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What is a Parabolic Reflector What is a Parabolic Reflector. The parabola is special type of curve that has a focal point to which parallel beams of light will be reflected. The opposite is also true, a light source placed at the focus will create a parallel beam of light, as in a spotlight. A parabola is the shape of the path of a projectile fired into the air and allowed to fall again (assuming no friction from the air), or a stone that is thrown into the air. It is also the shape obtained if you were to cut a cone shape along a line parallel to it's side.
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The 10 Highest Paid Moguls In Hollywood Follow Business Insider: With a $95 million/year paycheck, Howard Stern only ranks No.7 on Forbes' list of highest paid celebrities. Another day, another Forbes list. After ranking the highest paid DJs in the world last week, the publication has now put together a list of the Highest Paid Celebrities in Hollywood. Oprah Winfrey remains a top contender despite her lack of a daily presence on TV as of late, while big Hollywood directors and producers round out the list.
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Hyperbola Hyperbola as plane section of a cone Hyperbola (red): two views of a cone and two Dandelin spheres d 1, d 2 The intersection of an upright double cone by a plane not through the vertex with slope greater than the slope of the lines on the cone is a hyperbola (see diagram: red curve).
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Axis of Symmetry of a Parabola Every parabola has an axis of symmetry which is the line that runs down its 'center'. This line divides the graph into two perfect halves. Explore how the graph and equation relate to the axis of symmetry, by using our interactive program below.
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- Parabola. A u-shaped curve with certain specific properties. Formally, a parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix. Note: It is a common error to call any u-shaped curve a parabola.
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Parabola Here are the important names: 1  the directrix and focus (explained above). 2  the axis of symmetry (goes through the focus, at right angles to the directrix). 3  the vertex (where the parabola makes its sharpest turn) is halfway between the focus and directrix.
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- LINK / CITE ADD TO WORD LIST. adjective. The definition of parabolic is expressed as a parable, or bowl-shaped. 1  An example of something parabolic is the lesson in Jesus' tale of the Good Samaritan. 2  An example of something parabolic is a sattaline dish.INK / CITE ADD TO WORD LIST. adjective. The definition of parabolic is expressed as a parable, or bowl-shaped. 1  An example of something parabolic is the lesson in Jesus' tale of the Good Samaritan. 2  An example of something parabolic is a sattaline dish.
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Parabolic reflector Strictly, the three-dimensional shape of the reflector is called a paraboloid. A parabola is the two-dimensional figure.
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- Vertex of a Parabola. A parabola is the shape defined by a quadratic equation. The vertex is the peak in the curve as shown on the right. The peak will be pointing either downwards or upwards depending on the sign of the x 2 term.
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Quadratic Functions a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero Parabola a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve
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- Define parabolic. parabolic synonyms, parabolic pronunciation, parabolic translation, English dictionary definition of parabolic. also par·a·bol·i·cal adj. 1. Of or similar to a parable. 2. Of or having the form of a parabola or paraboloid. par′a·bol′i·cal·ly adv. adj 1.
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Key Vocabulary 1 : Quadratics To form a parabola according to ancient Greek definitions, you would start with a line and a point off to one side. The line is called the directrix; the point is called the focus. The parabola is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus.
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Parabola If the parabola instead opens upwards, its equation is. (6). Three points uniquely determine one parabola with directrix parallel to the-axis and one with directrix parallel to the-axis. If these parabolas pass through the three points, , and, they are given by equations.
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curve , plane curve consisting of all points such that the difference between the distances from any point on the curve to two fixed points (foci) is the same for all points..... Click the link for more information.; parabola parabola, plane curve consisting of all points equidistant from a given fixed point (focus) and a given fixed line (directrix).
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- f ( x ) = a x 2 + b x + c , a ≠ 0 {\displaystyle f(x)=ax^{2}+bx+c,\quad a\neq 0}. in the single variable x. The graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the y-axis, as shown at right.
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Axis of symmetry and vertex All parabolas have an axis of symmetry. The axis of symmetry of the parabola. y = ax 2 + bx + c. is the line y =. The vertex of a parabola is where the axis of symmetry intersects the parabola, so the x-coordinate of the vertex is the value of the axis of symmetry.