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Additional Solving Subtleties From §2.6 using the TI–84+ 3 §2.6 # 30; Confirm algebraic solution graphically: x 5x2 9 ; Algebraic Solution: x i 2 Big Idea: Only real solutions will show when graphed on the TI–84+. Imaginary solutions will not be visible on the graph, since we are graphing in the Real Number System. Using Technique 1. Screen shot from older OS. Using Technique 1. Screen shot from newer OS. Y1 and Y2 graphed in Standard Zoom. Note: When entering a square root, the calculator will give you the starting parenthesis and you will have to enter the ending parenthesis. Note: No parenthesis needed. Just right arrow out from under the square root. No intersection points, means NO REAL SOLUTIONS. Only Imaginary Solutions, if any. 3 Algebraically we got: x i . That 2 is we have algebraically, we have only imaginary solutions. Using Technique 2. Screen shot from older OS. Note: When entering a square root, the calculator will give you the starting parenthesis and you will have to enter the ending parenthesis. Using Technique 2. Screen shot from newer OS. Note: No parenthesis needed. Just right arrow out from under the square root. Math 114 – Additional Solving Subtleties 2.6 on TI–84+ Y3 graphed in Standard Zoom. NO x–intercepts means no real roots, that is, no real solutions of our original equation. Only Imaginary Solutions, if any. 3 Algebraically we got: x i . 2 That is we have algebraically, we have only imaginary solutions. Page 1 of 2 §2.6 # 22; Confirm algebraic solution graphically: 10 x 1 8 0 ; Algebraic Solution: No Solution Big Idea: Using Technique 2, “No Solution” means “No x–intercepts.” Here we illustrate only Technique 2 Using Technique 2. Screen shot since the equation is already set from newer OS. equal to 0. This screen shot is from the older OS. Y1 graphed in Standard Zoom. The majority of the graph is not visible, but we picked up a piece of it at the top of the y–axis that appears to be around the point (0, 9). In reality this is our y– intercept. To verify a y–intercept of (0, 9)… Let x = 0, then simplify to get a y–value of 9 for y1. Since we picked up only a small piece of the graph, let’s change the viewing rectangle to go higher on the y–axis. Using your grey WINDOW button, make the following change to Standard Zoom. Arrow down, and change the Ymax value. Set Ymax = 20. Then hit GRAPH. This is the upper half of a parabola opening to the right, with a y–intercept of (0, 9). There are NO x–intercepts, so we have NO real solutions. Looking only at the graph, and not at the algebra, it is possible that we might have complex conjugate imaginary solutions that we can’t see graphically, but algebraically we got back No Solution (No Real Solution AND No Imaginary Solution) which is consistent with this graph. Math 114 – Additional Solving Subtleties 2.6 on TI–84+ Page 2 of 2