The function y = x² and its graph
Make a table of values for y = x², plot the points, learn the properties of the graph and solve x² = 4 and x² = x + 2 from the graph.
- أوكرانيا: الصف ٨
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
In the Ukrainian programme this topic is in Grade 8 algebra: section 1, item 11, 'The function y = x² and its graph'. The area of a square with side x is y = x². That is the function y = x٢: each x has one value of y.
To draw the graph, make a table of values for x from -3 to 3, mark the points (x, y) on the plane and join them with a smooth curve. The graph is called a parabola.
Properties: it passes through (0, 0); it is symmetric about the y-axis since x and -x give the same y; all its points are on or above the x-axis, so y is at least 0; the least value of the function is 0 at x = 0.
To solve x٢ = a by the graph, find the x-coordinates of the points where the graph y = x² meets the line y = a. If a > 0 there are two roots, if a = 0 one, if a < 0 none. To solve x٢ = x + ٢, find where y = x² and y = x + 2 meet.