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Simultaneous Equations - Graphical Representation

Author:Beena Mavani
Topic:Equations

Simultaneous Equations involving a variables of degree 2

First solve these equations algebraically and . After find the solutions for x and y, check show function to show the graphs, then check show intersection to show the (x,y). In others the solution of simultaneous equations is / are the points of intersections of graphs in this case a parabola and a straight line.

Investigation

Change the value 'm' and 'c' to 0. Observe what are the intersection points. Jot down the values. Do you find anything interseting ? or what these values are called with respect to a function or an equation?

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Investigation #2

Let us continue with 'm'= 0 and change 'c'. Thus the straight line will be parallel to ? quadratic equation continue to be move 'c' to -1, -2 , - 3. jot down straight line equation and the corresponding points of intersection. you can further go up i.e. by moving 'c' to positive values. Again jot down the points of intersection.

Investigation # 3

Continue with 'm' = 0 and play around with 'c' only. For what values of 'c' such the x-values are always positive? What happens when c = 6?

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Investigation # 4

What happens when c= 7 ? How can you generalise?

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Exam Question

For what values 'c' of and such that f(x) and g(x) do not intersect in a real Cartesian plane?

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