Today is our topic of discussion Quadratic Function .
Quadratic Function
A quadratic function is a function which can be described by the equation y = ax²+bx+c where a, b and c are real numbers and a 0. Suppose, in this function a = 1, b = −4, c = −1. So y = ax² + bx+c can be written as y = x²-4x-1. We can get the related values of x and y from the described function which is shown in the following table.
This is the required graph of the quadratic function. Let’s observe some general properties of this quadratic function.
1) The graph is paraboloid shaped.
2) Symmetric point may be found about y axis or parallel to the y axis.
3) The value of the function will be maximum or minimum at a certain point.
Graph of a Circle
Noted that p, q and r are constants and if r 0 then in R, the graph of a relation S = {(x, y): (x − p)² + (y − q)² = r²} is a circle whose centre is the point (p,q) and radius is r (see the Mathematics book of class 9-10). In the graph paper, by plotting the point (p,q) as centre and taking r as radius we can draw a circle which will make the graph.
Remark: If the solution set of a relation is infinite, the known system of drawing its graph is to plot sufficient numbers of representative points of solution in the graph paper and then to join them, so that the graph of the relation can be clear. But if the graph of relation is a circle, using compass will make the work easier and beautiful, so we use the latter means.
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