real life example of a parabola?
921378
Projectiles without the presence of air pressure creates a parabolic trajectory (path taken by a projectile).\n\n^_^
310430
From a parabola, (k,h) would be where the vortex of the parabola is in the plane.
433311
I really like the parabola, but the ellipse is pretty cool too.
392380
All kinds of simple, easy calculus examples in real life (especially engineering!).  These depend on the level of math knowledge, but for University Calc. II:\n\nOptimization: (i.e. give a box with a volume, find minimum surface area) or (here's a certain amount of fencing, make the largest enclosure you can).  (Lagrangian Multipliers? did I even spell that right?  We looked at those when there are a lot of constraints on the problem (i.e. relationship between box dimensions must follow .....).\n\nForces: for example, average fluid pressure on a dam, given a function of distributed force, or fluid pressure on a submerged object. (Can be done in single or multiple integrals).\n\nRelated Rates:  i.e. two cars approach at right angles, different speeds, when will they meet.  Or, dropping a ball near a light source, find speed of shadow as function of angle made with light source, distance from ground, etc.  Differetial calculus example.\n\nArea and Volume: Double and triple integrals to find the volumes and areas of shapes. (Or single integrals, volumes of revolution, areas from curve to axis, if multi-variable calculus not covered).\n\nCurve Fitting: really good real-life use, take a set of data points from an experiment, select a curve type (i.e. quadratic, cubic, straight line, logarithmic, etc) and use minimization to get the best curve fit (set up an equation for the residuals, sum of (function) - (data point), and take derivatives with respect to each unknown coefficient in the function, set all derivatives equal to zero, solve simulatneously for curve coefficients. Now we can predict the outcome of the experiment at intermediate values, (as long as the curve fit is good).\n\nCentre of Mass, Centroids, etc: Find the balancing point on certain objects or groups of objects using integration. Can be single or multiple integrals, depending on complexity of shape.\n\nFields:  i.e. graviational fields, electrical fields, etc.  Or make up some fields.  Integration to find work required by a particle to traverse a path through some field.  Conservative and non-conservative fields.  Can use as an example of energy needed to move satellites along paths (equations) in space near earth's gravity, an electron through an electrical field, etc.  I guess some of these examples the field is conservative and it becomes kinda trivial if you work with end points, but don't have to.\n\nThese are some of the applications we used in our Calculus II-type course.  The hardest part is always setting the problem up, not solving, (which makes for good application problems I guess).  If multi-variable calculus isn't covered yet, then some of these examples would be kinda rough (i.e. fields).  Anyway, hope these are useful. \n\nCheers,
713002
Quite an old example, and one of the best-known, is the so-called Pell equation X^2 - D.Y^2 = -1 or +1, where D is a square-free integer and X, Y are both to be integers.  For example, when D = 3, there is no solution when -1 is on the right-hand side, but the solutions when it is +1 are (X, Y) = (2, 1), (7, 4), (26, 15), (97, 56), . . . an infinite series of integer pairs constructed by a simple rule starting from the first one (X' = 2X + 3Y, Y' = X + 2Y).
1004086
A parabola is a shape formed by all the points that are an equal distance from a line, called the directrix, and a point, called the focus. The interesting thing about parabolas is if you have a three-dimensional figure formed by rotating a parabola on its vertex, if you place a light source at the focus, the light that shines back and hits the parabolic surface will be reflected outward in parallel lines, creating a strong beam. This is how flashlights work. Also, if you use a parabolic shape for an antenna, signals coming in from space or whatever will hit the surface of the parabola and all be reflected onto the focus. If you put a receptor there, you will receive a very strong signal. That's a couple real life uses of parabolas.
423719
If your parabola is the standard y = ax^2 + bx + c, your domain should be all real x.  Since you mentioned that it opens up, your range goes to infinity.  Since your axis of symmetry is at (2, -1), your vertex is at (2, -1) and your lower y-bound is -1.\n\nBTW, the axis of symmetry is a line of the form x = 2, if I'm interpreting your information correctly.  The vertex of a parabola always lies on the axis of symmetry, which is why I assumed that your lower y-bound is -1 in finding the range.
1081487
A parabola opening down with a max at the point 0,-2.  it will also be twice as wide as a standard parabola
563653
the opposite of a hyperbola\nlike a PARAchute or umbrella, where the angle is more than 90 degrees, a hyperbola has an angle less than 90 degrees like a tulip.\n\nA satellite dish is a parabola
729616
Could you give a few examples please?
685803
I was just looking for this this morning for my class!\n\nTry a search using words like:\nquadratic practical example application\n\nFirst of all, realize that a quadratic equation deals with "squares" both literally and in reality. So, think about a problem where the shape of a square is involved. \n\n1. For example, what size of piece of cardboard would you need to make a box of some desired volume? \n\n2. Anytime you have a movement in one direction with a resistance (wind, wheel friction, etc.) in any other direction, a quadratic equation might be useful.\n\n3. Whenever something is rising or falling and a gravity has an effect on its movement, a quadratic equation applies and can be useful.\n\n4. Also, any situation where you have matching of every member of a group with all the others of the group, like the classic handshaking problem or a sports round robin.\n\nGood luck with the assignment and remember that mathematics is the only set of rules that everything must obey and if you do it right and use it only for the purposes it is intended for, it will never lead you astray. Mathematics can theoretically be used for any real world situation but the trick is knowing when mathematics is the fastest or best way. Other ways are estimation, trial and error, and asking someone with experience.
919933
I assume this is equal to y?\n\nIf it is, it's definitely a maximum because it's a parabola that opens downward\n\nNow I'll work on the vertex
771223
Strange parabola.\n\nBring the form to x = a(y-h)^2 + k\nThe vertex is (h,k).\nThe directrix will be x = k - m\nwhere m = 1/(4a)
303208
You are referring to locus/parametrics. The shape you are referring to in relation of a locus of a point and a line, is a PARABOLA. It looks like an curve/hill kinda thing.
449789
See for example these places:\n\nhttp://www.analyzemath.com/\n(Interesting interacctive math. graphics)\n\nhttp://mcraefamily.com/MathHelp/\nhttp://mcraeclan.com/MathHelp/GeometryHyperbolicTrigFunctions.htm
815141
You can find a bunch of them in this website:\nhttp://www.mathpuzzle.com/
1136350
Good Question, Mandelbrot's book and Barnsley's book will provide you with many examples.