Consider the case in which the constant A equals 16. Plot the graph of y=16x2 .

Part A Learning Goal: To understand and use inverse-square relationships. Consider the case in which the constant A equals 16. Plot the graph of y = = 16 Two quantities have an inverse-square relationship if y is inversely proportional to the square of x. We write the mathematical Plot points for x equal to one, two, three, four and five. relationship as y = - + . + Here, A is a constant. This relationship is sometimes written as y x x 2. SCALING Inverse-square scaling means, for example: No elements selected 20.0 . If you double x , you decrease y by a factor of 4. . If you halve x , you increase y by a factor of 4. . If you increase x by a factor of 3, you decrease y by a factor of 9. 16.0 . If you decrease x by a factor of 3, you increase y by a factor of 9. Generally, if a increases by a factor of C, y decreases by a factor of 12.0 C2. If a decreases by a factor of C, y increases by a factor of C2. RATIOS For any two values of x, for instance x1 and x2, we have 8.0 y1 = 2 and y2 = * ? Dividing the y1-equation by the y2-equation, we find 4.0 y1 A $2 2 2 y2 A/x2 72 A 0 2 That is, the ratio of y-values is the inverse of the ratio of the squares of the corresponding values of x. LIMITS As a becomes large, y becomes very small; as a becomes small, y becomes very large. Select the elements from the list and add them to the canvas setting the appropriate attributes. Press (CTRL+M ) to get to the main menu