Showing posts with label graph. Show all posts
Showing posts with label graph. Show all posts

Friday, April 26, 2013

Circles

A circle is the set of points equidistant from a fixed point called the center. The distance from the center to any point is called the radius.  Recall the following formulas from Geometry:
 

The circumference can be thought of as the perimeter of the circle.  In this section, we will be interested in the equations that describe circles.
 
From the equation of a circle in standard form we can see that a circle is completely determined by its center and radius.  In addition, notice that it is not a function because it fails the vertical line test.
[ InteractiveCircles ]

Given the equation of a circle in standard form, you can graph it using the following steps:
  1. Plot the center (hk).
  2. Use the radius r to plot four points up, down, left and right of the center.
  3. Connect the points and label them.
 
Even though a circle is not a function, it is a relation and we could still find the domain and range.  In addition, we will be asked to find the x- and y-intercepts.  This particular example does not have any but the technique to find them is the same method used throughout this study guide.


To find y-intercepts set x = 0 and solve for y.
To find x-intercepts set y = 0 and solve for x.


Graph the circles and label the x- and y-intercepts.
 

 
 
 
  
  
Graphing circles in standard form is just a matter of identifying the center and the radius.  The difficulty comes when the circle is not given in standard form.  In this case, when given general form, we will complete the square twice as illustrated below.
  1. Group all terms with variable x and group all terms with variable y.
  2. Complete the square for each grouping.
  3. Be sure to add (b/2)^2 to both sides of the equation.
Rewrite the circles in standard form and identify the center.
 
Find the area of the following circles.
 
Graph and find the x- and y-intercepts, area, and circumference.
 
Given the center and radius, find the equation of the circle.
 
YouTube Videos:





Thursday, April 25, 2013

Interactive: Perpendicular Lines


Interactive Instructions: Move the green points to change m and see that perpendicular lines have opposite reciprocal slopes.



[ NOTESPerpendicular Lines ]


Tuesday, April 23, 2013

Interactive: Slope-Intercept Form



Interactive Instructions: Slope-intercept form: y = mx + b. Move the green points to change m and b.





Saturday, March 23, 2013

Elementary Algebra Exam #2

Click on the 10 question exam covering topics in chapters 3 and 4. Give yourself one hour to try all of the problems and then come back and check your answers.


Graph. Also, find and label both the x- and y-intercepts.
 
Are the following lines parallel, perpendicular, or neither? Justify your answer.
 

Find the equation of the line:
 
 

  

 9. A light aircraft, flying with the wind, can travel 270 miles in 2 hours. On the return trip, flying against the same wind, the plane can only travel 210 miles in the same amount of time. What is the speed of the wind?
10. Marcia invested a total of 2,500 dollars in two separate accounts. One account earned 6% annual interest and the other earned 8%. If her total interest for the year was 167 dollars, then how much did she invest in each account?
 
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