Unbelievable shapes can be created by using the implicit plotting capabilities of a computer algebra systems. Use a graphing calculator or graphing system to graph the curve: y(v -1)(v–2)=x(x-1)(x-2). Include an image or sketch of the resulting graph. 1. At how may points does this curve have horizontal tangent lines? Estimate the x-coordinates of these points. 2. Find the equations of the tangent lines at the points (0,1) and (0,2) 3. Find the exact x-coordinates of the point where the curve has horizontal tangent lines. 4. Create even more fanciful and unbelievable curves by modifying the equation. Include the modified equation and a sketch or image of the graph.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.