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Pre-CalculusLesson 1: Algebra RevisitedFormulas, definitions, and methods from Algebra 1
The distance d between any two points with coordinates and is given by the formula d = .
The Distance Formula
1 1( , )x y 2 2( , )x y
2 22 1 2 1( ) ( )x x y y
Applying the Distance Formula Find the distance between (-3, 2) and (4, 1)
Applying the Distance Formula Find the distance between (-3, 2) and (4, 1)
( 3 4)2 (2 1)2d =
Applying the Distance Formula Find the distance between (-3, 2) and (4, 1)
( 3 4)2 (2 1)2d =
( 7)2 (1)2 49 1d =
Applying the Distance Formula Find the distance between (-3, 2) and (4, 1)
( 3 4)2 (2 1)2d =
( 7)2 (1)2 49 1d =
50 or 5 2 or 7.07d =
In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and are .
Midpoint Formula
1 2 1 2,2 2
x x y y
1 1( , )x y 2 2( , )x y
Applying the Midpoint FormulaFind the midpoint between (-2, 5) and (6, 4)
Applying the Midpoint FormulaFind the midpoint between (-2, 5) and (6, 4)
2 62
,5 4
2
M =
Applying the Midpoint FormulaFind the midpoint between (-2, 5) and (6, 4)
42
,92
= 2,
92
M =
2 62
,5 4
2
M =
Domain and RangeDomain = the input of a functionRange = the output of a function
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
Evaluating FunctionsTo evaluate a function, simply
replace (substitute) the function's variable with the indicated number or expression.
Evaluating FunctionsTo evaluate a function, simply
replace (substitute) the function's variable with the indicated number or expression.
f(x) = 2x + 5, Find f(3).
Evaluating FunctionsTo 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.
Evaluating Functions
Evaluating Functions
Evaluating Functions
Evaluating Functions
Slope Formula:
12
12
xx
yym
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
Find the slope of the line that goes through the points (-5, 3) and (2, 1).
m y2 y1
x2 x1
Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS
Find the slope of the line that goes through the points (-5, 3) and (2, 1).
m y2 y1
x2 x1
1 3
2 ( 5)m
Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS
Find the slope of the line that goes through the points (-5, 3) and (2, 1).
m y2 y1
x2 x1
1 3
2 ( 5)m
1 3
2 5m
Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS
Find the slope of the line that goes through the points (-5, 3) and (2, 1).
m y2 y1
x2 x1
1 3
2 ( 5)m
1 3
2 5m
2
7m
Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS
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
Equation of a CircleThe circle with center (0,0) and radius r is the graph of the equation
222 ryx
Equation of a CircleThe circle with center (h,k) and radius r is the graph of the equation:
222 rkyhx
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
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 = 2Write the equation of a circle
centered at (5,1) with a radius of 5
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 = 2Write the equation of a circle
centered at (5,1) with a radius of 5 (x − 5)2 + (y – 1)2 = 25
Extension ProblemWrite the equation of the circle whose diameter extends from the point (-2,1) to the point (6,-5).
