1. Pre-Calculus Lesson 1: Algebra Revisited Formulas, definitions, and methods from Algebra 1

2. The distance d between any two points with coordinates and is given by the formula d =. The Distance Formula

3. Applying the Distance Formula Find the distance between (-3, 2) and (4, 1)

4. Applying the Distance Formula Find the distance between (-3, 2) and (4, 1) d =

5. Applying the Distance Formula Find the distance between (-3, 2) and (4, 1) d =

6. Applying the Distance Formula Find the distance between (-3, 2) and (4, 1) d =

7. In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and are. Midpoint Formula

8. Applying the Midpoint Formula Find the midpoint between (-2, 5) and (6, 4)

9. Applying the Midpoint Formula Find the midpoint between (-2, 5) and (6, 4) M =

10. Applying the Midpoint Formula Find the midpoint between (-2, 5) and (6, 4) M =

11. Domain and Range  Domain = the input of a function  Range = the output of a function

12. Vertical Line Test:  If a vertical line can connect two points on the graph of a relation, then the relation is not a function.  Examples: http://math.tutorvista.com/calculus/vertical-line-test.html

13. Evaluating Functions  To evaluate a function, simply replace (substitute) the function's variable with the indicated number or expression.

14. Evaluating Functions  To evaluate a function, simply replace (substitute) the function's variable with the indicated number or expression.  f(x) = 2x + 5, Find f(3).

15. Evaluating Functions  To evaluate a function, simply replace (substitute) the function's variable with the indicated number or expression.  f(x) = 2x + 5, Find f(3).  f(3) = 2(3) + 5 = 11.

16. Evaluating Functions

20. Slope Formula:

21. Find the slope of the line that goes through the points (-5, 3) and (2, 1). Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

22. Find the slope of the line that goes through the points (-5, 3) and (2, 1). Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

23. Find the slope of the line that goes through the points (-5, 3) and (2, 1). Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

24. Find the slope of the line that goes through the points (-5, 3) and (2, 1). Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

25. Find the slope of the line that goes through the points (-5, 3) and (2, 1). Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

26. A few things to remember about circles:  A circle is a set of points equidistant from a central point.  A circle is named using its center point.  Radius=distance from center to edge of circle.  Diameter=2 x radius

27. Equation of a Circle The circle with center (0,0) and radius r is the graph of the equation

28. Equation of a Circle The circle with center (h,k) and radius r is the graph of the equation:

29. Applying the Equation of a Circle  Identify the coordinates of the center and the length of the radius in the circle (x − 5) 2 + (y + 2) 2 = 4  Write the equation of a circle centered at (5,1) with a radius of 5

30. Applying the Equation of a Circle  Identify the coordinates of the center and the length of the radius in the circle (x − 5) 2 + (y + 2) 2 = 4 (5, -2), r = 2  Write the equation of a circle centered at (5,1) with a radius of 5

31. Applying the Equation of a Circle  Identify the coordinates of the center and the length of the radius in the circle (x − 5) 2 + (y + 2) 2 = 4 (5, -2), r = 2  Write the equation of a circle centered at (5,1) with a radius of 5 (x − 5) 2 + (y – 1) 2 = 25

32. Extension Problem Write the equation of the circle whose diameter extends from the point (-2,1) to the point (6,-5).