Dawnbridge

TI-84 Plus CE field manual for IB Math

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16

Finding roots of a function

All courses

Plot a function, widen the x-window until every x-intercept is on screen, then use the calculator's root / zero tool to read each solution.

Goal

Find every root of y=ln(x+2)12x0.8.

1

Press and type the function on Y1: .

2

Start on the standard window: press (6: ZStandard). One root is visible near x0.278, but the graph is still above the x-axis at the right edge of the screen, so this view is too narrow to be sure there is only one root.

NORMALFLOATAUTOREALRADIANMP
3

Widen the view to check the right side: press (3: Zoom Out) and then once. With the default factor 4, the window expands from [-10,10] to [-40,40], wide enough to reveal the second crossing near x33.1. The downside is the y-range also expands, squashing the curve against the x-axis.

NORMALFLOATAUTOREALRADIANMP
4

Crop back in with a box: press (1: ZBox). Anchor one corner above-left of the curve's strip with , then move below-right (keeping both crossings inside the marquee) and press again. The window snaps to the box, keeping the full x-coverage but restoring a readable y-scale.

NORMALFLOATAUTOREALRADIANMP
5

Read off the near root: press (2: zero). At Left Bound? move just left of the crossing and press ; at Right Bound? move just right of it and press ; at Guess? move near the crossing and press . The calculator jumps to the zero and prints its coordinates.

NORMALFLOATAUTOREALRADIANMP
Zero
X=0.2776311376 Y=0
6

Repeat CALC (2: zero) for the second root, the crossing on the right side of the screen. Bracket it the same way: left bound, right bound, then guess.

NORMALFLOATAUTOREALRADIANMP
Zero
X=33.0975894 Y=0
Result

The roots are approximately x0.278 and x33.1.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Find all real roots of f(x)=x34x+1.

  2. 2

    Find all real roots of f(x)=ex3x2.

  3. 3

    Find all real roots of f(x)=ln(x+3)x2.