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HOW TO FIND THE ROOT OF A FUNCTION WITH TI89 CALCULATOR

Steps Key Sequence Screens
1. Input Function or Piecewise-Defined Function. Press DIAMOND key, then F1 key (for Y=)
  Type the function
Method 1: Using home screen.
2. Go to Home screen Press 2nd, then ESC
3. Select zeros function Press F2
  Press 4 (for zeros()
4. Type in Function  
Note: You can either type in the function directly (e.g., 5 – 2x2 + x3) OR, if you followed step 1 above, use y1(x)
4. Type in Independent Variable Press comma key, then x, then right parenthesis
Note: This will find ALL zeros of the function on the whole domain of the function.
5. Solve ENTER
Note: If this returns something other than a value, then press DIAMOND key, then ENTER. Alternatively, you can use the TI89's solve function.
 
Method 2: Using grapher.
Follow Step 1 above    
  Type the function
2. Graph Press DIAMOND key, then F3 key
3. Find in Press F5
  Press 2 (for Zero)
  Type in x-value for a point to the left of x-intercept or trace function until you reach the value for x
  Press ENTER
  Type in x-value for a point to the right of x-intercept or trace function until you reach the value for x
  Press ENTER
Note: In this case, the root of the function is x = –1.2419.