Concept Byte: Finding Roots

Use With Lesson 9-3

TECHNOLOGY

The solutions of a quadratic equation are the x-intercepts of the graph of the related quadratic function. Recall that the solutions and the related x-intercepts are often called roots of the equation or zeros of the function.

Activity

Use a graphing calculator to solve x 2 − 6 x + 3 = 0 . x squared , minus 6 x plus 3 equals 0 .

• Step 1 Enter y = x 2 − 6 x + 3 y equals . x squared , minus 6 . x plus 3  on the Y = cap y equals  screen. Use the CALC feature. Select ZERO. The calculator will graph the function.

• Step 2

  Move the cursor to the left of the first x-intercept. Press enter begin box , enter , end box  to set the left bound.

• Step 3

  Move the cursor slightly to the right of the intercept. Press enter begin box , enter , end box  to set the right bound.

• Step 4

  Press enter begin box , enter , end box  to display the first root, which is about 0.55.

Repeat Steps 2–4 for the second x-intercept. The second root is about 5.45. So the solutions are about 0.55 and 5.45.

Suppose you cannot see both of the x-intercepts on your graph. You can find the values of y that are close to zero by using the TABLE feature. Use the TBLSET feature to control how the table behaves. Set Δ TBL cap delta  to 0.5. Set INDPNT: and DEPEND: to AUTO. The calculator screen below shows part of the table for y = 2 x 2 − 48 x + 285 . y equals , 2 x squared , minus 48 x plus 285 .

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Exercises

Use a graphing calculator to solve each equation. Round your solutions to the nearest hundredth.

1. x 2 − 6 x − 16 = 0 x squared , minus 6 . x minus 16 equals 0
2. 2 x 2 + x − 6 = 0 2 x squared , plus x minus 6 equals 0
3. 1 3 x 2 + 8 x − 3 = 0 1 third , x squared , plus 8 x minus 3 equals 0
4. x 2 − 18 x + 5 = 0 x squared , minus 18 . x plus 5 equals 0
5. 0.25 x 2 − 8 x − 45 = 0 0.25 , x squared . minus 8 x minus 45 equals 0
6. 0.5 x 2 + 3 x − 36 = 0 0.5 x squared . plus 3 x minus 36 equals 0

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