Solving an equation? Here are some handy ways to do so, and each has its advantages

First, get zero on one side of your equation by hand. Enter the expression that equals zero in the "Y=" screen. Push [2ND/TRACE] and scroll down to choose zero. You will see a graph. Make sure that your window is appropriate to see where the graph crosses the x-axis. Use the left and right arrows to pick an x value that puts you closely to the right of the x-intercept and push ENTER. Do the same on the left side of the x-intercept. You may now enter a guess, or just push ENTER again. It will calculate the zero which is the solution. Be aware that there could be multiple x-intercepts with multiple solutions.

Your equation will have an expression on each side. Go to the "Y=" screen and enter each side as a separate Y= expression. Press [2ND/TRACE], and it will prompt you to pick the graphs for which you want intersections. Find the intersection you'd like to know, and enter places on each graph close to it. This will be the solution. Note that there may be more than one, and you'll need to find each separately.

Need to explore an equation or graph? This is the starting point. This is your entrance to graphs, tables, and it even stores an expression as a Y-VAR.

Once you have an expression in the Y= screen, go back to the main screen. Press VARS, move over to Y-VARS, and select Function... This will call up that expression in your calculations. Note: you need to remember which Y= expression you want, because it will not show the expressions when you choose which one to call up.

In the "Y=" screen, choose a Y= expression. Put that entire expression in parentheses. Then divide it by your domain restriction. Example: If you only want the expression 3x+2 evaluated for x>5, then enter (3x+2)/(x>5). Find the inequality signs by pressing 2ND, and then MATH. You can enter piecewise functions as individual Y= expressions with individual domain restrictions.

Find and select MODE. Find the FUNC PAR POL SEQ section, and select PAR (for parametric mode.) Now go back to the Y= screen, and notice that there are X= and Y= pairs that are ready for entries in terms of T. The motion of a normal function can be shown in the x-direction by inputting the function in terms of t for the X= section. Choose a constant for Y= that will fit nicely in the window. For instance, plot a function with a window of -100 < x < 100 and 0 < y < 2, and choose 1 for the Y= constant. Also in the window, choose a good range of input values that will show the motion. These will be the T-values.

Tables are under-appreciated for what they can do.

If you have an expression in the "Y=" screen, simply press [2ND/GRAPH] to bring up its table. To find the average slope between any two points, just use the slope formula: m = (y2-y1)/(x2-x1).

Say you have f(x) in the "Y=" screen and you want to find f(2.9) and f(3.1). Press [2ND/WINDOW] to get to the Tableset screen. Choose a handy starting point (maybe 2.9 or maybe 3). This will change later if you scroll through the table. Choose a handy x-step value (maybe 0.1 here). You'll get the values you want from the table without having to graph or re-enter information.

Your calculator crunches the numbers to estimate derivatives at given x-values, or definite integrals. It may not be perfect, but it is usually close enough (easily within a thousandth of the correct answer).

Find "nDeriv(" on the calculator. Try using the [MATH] button and scrolling down. After the parentheses, input the expression, then input the variable that the derivative is based on, and then input the value at which the derivative will be taken. Example: nDeriv(2x+3,x,2) takes the derivative of 2x+3 with respect to x at x=2. If your calculator has MATHPRINT on, then you will fill in the same information in the correct places as you might write it yourself. *Note: Any expression from the "Y=" screen can be inserted in "nDeriv(" using the "Getting an Expression from Y=" directions above.

Find "fnInt(" on the calculator. Try using the [MATH] button and scrolling down. After the parentheses, input the expression, then input the variable that the integral is based on, and then input the values at the beginning and end of the definite integral. Example: fnInt(2x+3,x,1,5) finds the definite integral of 2x+3 with respect to x on the interval from 1 to 5. If your calculator has MATHPRINT on, then you will fill in the same information in the correct places as you might write it yourself. *Note: Any expression from the "Y=" screen can be inserted in "fnInt(" using the "Getting an Expression from Y=" directions above.