Transcript Chapter_1[1] Chris M

Chapter 1: Linear and
Quadratic functions
By Chris Muffi
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Vocabulary◦
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Coordinates- ordered pair of numbers
x-axis- is the horizontal line
y-axis- is the vertical line
Origin- the x and y- axis point of origin
Quadrants- the axis divides them into 4 of
them
◦ Solution- is an ordered pair of numbers that
makes the equation true.
1-1 Points and Lines
1-1 Formulas to know
Mid-Point Formula:
M
 x1  x 2 y1  y 2 
=  2 , 2 
Distance Formula
Ab=
x2  x1 2   y2  y1 2
1-1 Example
Use A(4, 2), B(2, 10), C(-2, 9), and D(0,
1).
A. Show that AC and BD bisect each
other.
B. Show that AC = BC.
C. What kind of figure is ABCD?
D. Find the length of AC .
E. Find the midpoint of AC .
1-2 Slope of lines
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Slope
m
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rise y 2  y1

run x2  x1
Facts to know
◦ Horizontal lines have a slope of zero
◦ Vertical lines have no slope
◦ Negative slopes fall to the right
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y= mx + b is slope intercept form
Slope-intercept form
1-3 Equations of Lines
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Formulas:
◦ General Form
Ax + By= C
◦ Slope intercept Form
 y = mx + B
◦ Point Slope Form
y  y1
m
x  x1
◦ Intercept Form
x y
 1
a b
Function- describes a dependent
relationship between two quantities
 Linear functions have the form f(x) = mx
+B
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1-4 Linear Functions and
Models
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Domain- is the set of values for which the
function is defined. You can think of the
domain of a function as the set of input
values.
Domain
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The set of output values is called the
range of the function.
Range
1-5 Complex Numbers
Counting Numbers are 1, 2, 3..
 Rational Numbers are ratios of integers,
to represent fractional parts of quantities.
 Irrational Numbers are like these
2
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Complex
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These numbers are commonly
referred to as imaginary numbers.
And look like these  1 and  15
i  1
i   1  1  1
2
i   1  1  1  i
3
i  1 1 1 1  1
4
i  1 1 1 1 1  i
5
i   1ofImaginary
1  1  1  1  1  1
Pattern
6
1-6 Solving Quadratic Equations
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quadratic equation- equation that can be
written in the form ax 2  bx  c  0
where
a≠0
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Roots
◦ A root, or solution, of a quadratic equation is
a value of the variable that satisfies the
equation.
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completing the square- method of transforming a quadratic
equation so that one side is a perfect square trinomial
Steps:
◦ Step 1: Divide both sides by the coefficient of so that
will have a coefficient of 1.
◦ Step 2: Subtract the constant term from both sides.
◦ Step 3: Complete the square. Add the square of one
half the coefficient of x to both sides.
◦ Step 4: Take the square root of both sides and solve for
x.
Completing the Square
Quadratic Formula
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quadratic formula- derived by
completing the square.
 b  b 2  4ac
x
2a
1-7 Quadratic Functions
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a ≠ 0, is the set of points (x, y) that
satisfies the equation y  ax 2  bx  c then
this graph is a parabola
X and Y- Intercept
The y-intercept of a parabola with
equation y  ax 2  bx  c
is c.
 If b 2  4ac > 0, there are two xintercepts.
2
 If b  4ac = 0, there is one x-intercept
(at a point where the parabola and the
x-axis are tangent to each other).
2
 If b  4ac < 0, there are no xintercepts.
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