Graphing a Heart on your TI-84

Sookochoff’s Calculator Valentine

Here are the functions that will graph a heart in a window with an x-max is 10, x-min is -10, y-min is -7, y-max is 7).  To input the forward slash use the divide key and to input the inequality signs, press 2nd Math.  To use this as a learning opportunity, reflect on how one might graph a circle and a line and how I used these to make a heart.  Also, in the curly brackets, I have restricted the domain of the semi-circles and the lines.  Think about what you know about domain restrictions and how this is working here.  To see the effect of the domain restrictions, try viewing the graph without the domain restrictions.  NOTE CORRECTION:  I missed two negative signs when I posted this.  I have drawn them in with red pen.  Oopsy!

Math 30-1 students, ask yourself how I used transformations of a circle to make the first four functions.  Look ahead to conics to find our curriculum items related to circles and graphing.

All students: compare the Pythagorean Theorem to the functions that graph a circle.  A semi-circle with radius 3 can be graphed with y=sqrt(9-x^2) which comes from 3^2=x^2 + y^2.  Check out some youtube videos about how to graph a circle (a set of points equidistant from a given point.

More for All:  can you graph an arrow through this heart using y=mx+b?  Happy Valentines, everyone.

Challenge:  Can you figure out how to get rid of the extra bits of line at the bottom?  Or can you adjust the window so that the lines are only visible where you want them.

  1. Peter M says:

    Here is my solution to the chalenge

    Enter in the Y= menu

    Y2=\/(5.5 – (1.5X – 2.2)^2) +7
    Y3=\/(5.5 – (1.5X + 2.2)^2) +7

    • HI Peter,
      Nice job. I can see that you will get a rounded bottom on your heart with y1. And I’m not sure what those v’s mean in y2 and y3. Otherwise, I see that they are downward opening parabolas. Have you ever seen an absolute value function? To graph one, you need to MATH, arrow right to the NUMBERmenu and chose “abs(” Jusy try y=abs(x) and see how that might help you with y1. Thanks for your brave post.

  2. Hajar Ghalab says:

    interesting ^___^… kind of neat.. i want to try to do it but i have TI-83 i tried but it did not work >__<

  3. Lauren L. says:

    Y1 = x^2/3-(24-x^2)^1/2
    Y2 = x^2/3+(24-x^2)^1/2

  4. Ronald lorenzo says:

    How do you enter the 2nd math option on a ti-Nspire it doesnt allow me to input the less than and greater than options into equations i get “syntax error” ? Email me if possible please

  5. Jimmy says:

    Change the window to Ymin=-4

  6. Pedro says:

    In order to make the extra lines disappear:
    In y5, change the first “x” for “(sqrt(x))^2”. That way the domain is only IR 0+
    In y6, change the “-x” for”(sqrt(-x))^2″. This way the domain is only IR 0-

    • I think your second suggestion may be incorrect. Do you mean replace -x with -(sqrt(x))^2?

      • Pedro says:

        No, i don’t think it’s incorrect. In my ti84 it shows just fine! And it does make sense in the way that by adding the extra “-” you have the exact same symmetrical segment, with the axis at “x=0”. Try it for yourself! 🙂

  7. Ti 1111 says:

    Thank you so much, i´m going to surprise my loved one with this heart…
    BTW: i used 7.9 instead of 4.2 (the first one) for Y5 and Y6, because de V shape didn’t connect with the upper part of the heart.
    and again thank you so much, SHE will be surprised

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