In this section, quadratic equations with non-integral solutions are examined.

Example: Solve: - one-half 1 2 x² + 2x + 1 = 0

Step 1: Enter the equation into [Y=].

graphing calculator screen showing Y1=-1/2x^2+2x+1

Step 2: Go to the table.

Step 3: Use the up and down arrows to scroll up and down the table.

Between what x-values does - 1 2 x² + 2x + 1 = 0

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Check Your Answer

Between -1 and 0 and between 4 and 5

How did you determine where the solutions were located?

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Check Your Answer

First look at the y1 column. We know that 0 is between -1.5 and 1. Therefore, the corresponding x-values tell us that x must be between -1 and 0.

Step 4: Once you have narrowed down where the solution is located, you can examine the values between these numbers by changing the table interval in the TABLE SETUP window. Go to [2ND] [WINDOW].

Step 5: Change the table interval to tenths.

graphing calculator screen showing TABLE SETUP showing TblStart = -1 , ∆Tbl=0.1, and both Indpnt and depend set on Auto

Step 6: Now, go back to the table. Between what x-values does - 1 2 x² + 2x + 1 = 0?

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Check Your Answer

Since 0 is closer to 0.12 than -0.125, we can round the solutions to x = -0.4 or 4.4.

Now see if you can round to the nearest hundredth.

Hint: Since you know that the zero is between -0.5 and -0.4, enter one of these numbers for TblStart. This will reduce the amount of scrolling needed.

graphing calculator screen showing TABLE SETUP showing TblStart = -.05 , ∆Tbl=0.01, and both Indpnt and depend set on Auto

Interactive popup. Assistance may be required.

Check Your Answer

x = -0.45 or x = 4.45.