(Wednesday after the test)
Topics:
• Completing the square to put the equation of a parabola into its vertex form 
Reminder: The method we use, which the WeBWorK leads you through step-by-step, is not the method used in the textbook.
Here is a video from VirtualNerd which shows the method being used when the leading coefficient is 1. I have not been able to find a source that shows our method when the leading coefficient is not 1: the best thing to do is to work through the WeBWorK exercises (you can do this even if the assignment is closed) and make notes on the steps.
• Drawing the graphs of quadratic functions (parabolas).
To have a complete graph, you should show the following features;
• The vertex
• The axis of symmetry – you do not have to draw it in as a line, but you should make it clear that your graph is symmetric around a vertical line through the vertex
• The y-intercept: this is the point where x=0.
• The x-intercepts, if there are any. (They are the points where y=0.)
I also showed you a little trick that you can use to get two other points of the graph starting with the vertex, and using the leading coefficient a. My notes are here: MAT1275graphingParabolasPictures
Remember the effect of the number a on the graph: the parabola will be stretched away from the x-axis or compressed toward the x-axis depending on whether |a| is greater than 1 or less than 1 (between 0 and 1), and the parabola will open downward if a is negative.
• New topic: The Distance Formula
The distance formula is a result of the Pythagorean Theorem, and it will be easier to remember it correctly if you understand how we get it from the Pythagorean Theorem. Here is a nice video explanation from Khan Academy.
We use the distance formula to get to our next topic, which is
• Circles
Because the definition of a circle is that it is the set of all points in the plane which are at a fixed distance r away from its center (h, k), we can get an equation for a circle using the distance formula:
Or by squaring both sides,
This is the standard form of the equation of a circle with radius r and center (h, k).
In case the center is at the origin (0,0), the equation will have a particularly simple form:
We looked at Examples 1 and 2 in Chapter 9, where we had to read off the center and radius of the circle and use them to draw the graph. To help draw the graph we find four points on the circle: starting at the center, go up by the amount r, then down by the amount r, then right by the amount r, then left by the amount r. This makes it easier to draw a nice circle.
Homework:
• Review the examples we discussed in class. Make sure that you understand the derivation of the distance formula and the formula for the circle, as well.
• In Chapter 7, do problems #45-51 odd
• In Chapter 9, do the assigned problems from the Course Outline up to #37 only
• Do the WeBWorK: Two very short assignments due by Tuesday 11 PM, but do not wait to the last minute!
Remember that you can use the Piazza discussion board to ask questions if you get stuck on any of the WeBWorK or the other homework problems. Don’t forget to include the problem itself in your question, as that will make it easier for you to get a quick response!
