Math = Love: Finding X-Intercepts and Y-Intercepts

## Wednesday, January 13, 2016

### Finding X-Intercepts and Y-Intercepts

I am so behind on my Algebra 2 notebook.  Keeping up with notebooks for Algebra 1, Algebra 2, and Stats this year is killing me.  Actually, it killed me last year, too.  I need to get in the habit of gluing my notes in the notebook while my students are doing the same.  That just hasn't happened yet.

So, I realize I have a lot of notes to get caught up on and post to this blog.  But, I'm just going to jump in where we're at this moment.  We are learning about all the things our graphing calculators can do.  First up: finding the x-intercept and y-intercept of a graph.  These instructions are written for using a TI-84 because that's what I have a class set of.

As I was typing these up, I did a quick google to find if I could find something already typed up.  Nothing looked pretty enough to just print and glue in our notebooks.  But, in the process, I did learn a new way of finding the y-intercept using the calculator.  When I was in high school, my teacher taught us to always use the table on the calculator to find the y-intercept.  Y'all probably already know this, but you can also use the Value Option from the Calculate menu.  This was news to me!  I put both options down for my students.  Giving students multiple solving options is something I'm trying to do a better job of incorporating in my classes.

Another thing that throws my students off is the fact that they are rarely asked to find the y-intercept of a graph on their end-of-instruction exam.  Instead, they will be asked to find the roots, solutions, or zeros of an equation.  I really try to drive home the fact that anytime they are asked for roots, solutions, or zeros, they are really just being asked to find the x-intercept.

I told my students to draw a box around this fact, star it, add exclamation points, or anything that would make it stand out in their notes.  They noted that the way I had boxed it in on mine looked like the state of Oklahoma.  I joked that I had done that on purpose because the state of Oklahoma was requiring them to know this fact.

My students really struggled with the left bound and right bound instructions, so I shared with them a tip I learned from @druinok.  She has her students place the cursor as close to the point as possible and then click the left arrow a few times for left bound and the right arrow a few times for right bound.  My students thought this was the best trick ever.  It really cut down on the mistakes they were making.

If you think you could use these with your students, I've uploaded them here.

1. If you have know that an x-intercept is between two integers (ex: -2 and -1), you can type the lower x-value (-2) for the left bound, press enter, type the higher x-value (-1) for the right, press enter, and then press enter again.

The same thing will work for the bounds to find the minimum or maximum

1. Thanks for the tip! I keep learning new things. :)

2. If you have a student who is a fast finisher, they can be the ones to update your notebook. Or it could be a class job. Or for a little extra credit (though I'm not sure I'd trust the kid who needs extra credit to update the master notebook).

1. I love this idea, but I think I'm too obsessive about how my notebook looks to let it in the hands of a student. Sometimes I wish I wasn't so perfectionistic.

2. I have the same issue. But I have decided I may have a choice 2 or 3 students who I know will take notes the way I want them to be recorded. This way if I fall behind, I can snap a photo of their page and put it in my digital notebook

3. So we did this in class using quadratics (that we could graph by hand but now are testing out our technology skills).
I was wondering about whether to even teach using the graphing calc to find zeros. My students seem to always make mistakes with the left bound and right bound, especially if we are doing a contextual problem that involves a serious change to the window.
What do you think about treating finding the zeros as an intersection between the quadratic and the line y=0? Then they have to just find the intersection, which they can do much better. As long as they understand they are finding the zeros/solutions, would this work? Do any other readers think their students would be more successful this way?

1. When I taught with the TI-84, I taught finding the zeros with the intersection of the graph and y=0.

2. Very interesting! We haven't learned to find intersections *yet* on the calculator.

3. I know that, as a student, when I learned that finding the intersection with y=0 was the same as using the Zero function, I never used the latter ever again. Instead of scrolling left and right, you just move the cursor in the viscinity and press Enter three times. My students don't have graphing calulators, but if they did? It is so efficient that I would teach them about Intersection just so they could use it instead of Zero.

4. Thanks for this printable. I was just teaching this and my students would love this in their notebooks to look back at.

1. You're welcome! Glad someone else can use it!

5. I feel that I should point out that the Value function (in the Calc/2nd Trace menu) is also present in the Trace environment, itself. If you press Trace (rather than 2nd Trace), you can type a number followed by [Enter] and it will give you the same result as the Value function.

1. Thanks for sharing this helpful tip!

6. Thanks for the helpful lesson and information. I linked this page to a video I created on this topic. MooMooMath and Science
Cheers