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Precalculus

Find a maximum or minimum

Find the lowest or highest point of a curve, such as the vertex of y = x² − 2x.

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The lowest point on a smooth curve is a minimum and the highest is a maximum. For a parabola, this is the vertex.

The example y = x² − 2x has its minimum at (1, -1).

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Enter X² − 2X on y= and press graph.

    y=X,T,θ,nx²−2X,T,θ,ngraph

  2. Open the CALC menu (2nd then trace) and pick 3, minimum. (4 is maximum.)

    2ndCALCtrace3

  3. Left bound -5, enter. Right bound 5, enter. Then enter for the guess.

    (−)5enter5enterenter

You should seeMinimum X=1 Y=⁻1

Classic Graphing 84 key reference · Classic Graphing 84 manual

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Enter X² − 2X in the Graph app and draw it with F6.

    MENU3X,θ,Tx²−2X,θ,TEXEF6

  2. Open G-SOLV (F5) and press F3 for MIN. (F2 is MAX.)

    F5F3

You should seeMIN X=1 Y=-1

Natural Color Graphing key reference · Natural Color Graphing manual

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Graph x² − 2x. The ² key gives a power and the multiplication dot is implied between 2 and x.

    docxx²−2xenter

  2. Open the menu, choose 4, Analyze Graph, then 2, Minimum. (3 is Maximum.)

    menu42

You should seeminimum x=1 y=-1

Classic CAS key reference · Classic CAS manual

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