Chapter 1: Linear and Quadratic functions By Chris Muffi.
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Transcript of Chapter 1: Linear and Quadratic functions By Chris Muffi.
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Chapter 1: Linear and Chapter 1: Linear and Quadratic functions Quadratic functions
By Chris Muffi
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1-1 Points and Lines1-1 Points and Lines
Vocabulary-◦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.
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1-1 Formulas to know1-1 Formulas to knowMid-Point Formula:
M =
Distance Formula
Ab=
2,
22121 yyxx
212
212 yyxx
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1-1 Example1-1 ExampleUse A(4, 2), B(2, 10), C(-2, 9), and D(0,
1).A. Show that and bisect each
other.B. Show that AC = BC.C. What kind of figure is ABCD?D. Find the length of .E. Find the midpoint of .
AC BD
AC
AC
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1-2 Slope of lines1-2 Slope of linesSlope
Facts to know◦Horizontal lines have a slope of zero◦Vertical lines have no slope◦Negative slopes fall to the right
12
12
xxyy
runrisem
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Slope-intercept formSlope-intercept form
y= mx + b is slope intercept form
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1-3 Equations of Lines1-3 Equations of LinesFormulas:
◦ General FormAx + By= C
◦ Slope intercept Form y = mx + B
◦ Point Slope Form
◦ Intercept Formm
xxyy
1
1
1by
ax
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1-4 Linear Functions and 1-4 Linear Functions and ModelsModels
Function- describes a dependent relationship between two quantities
Linear functions have the form f(x) = mx + B
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DomainDomain
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.
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RangeRange
The set of output values is called the range of the function.
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1-5 Complex Numbers1-5 Complex NumbersCounting 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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ComplexComplexThese numbers are commonly
referred to as imaginary numbers. And look like these 15 and 1
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Pattern of ImaginaryPattern of Imaginary 1111111
11111
11111
111
111
1
6
5
4
3
2
i
ii
i
ii
i
i
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1-6 Solving Quadratic Equations1-6 Solving Quadratic Equationsquadratic equation- equation that can be
written in the form where a ≠ 0
Roots◦A root, or solution, of a quadratic equation is a
value of the variable that satisfies the equation.
02 cbxax
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Completing the SquareCompleting the Square
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.
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Quadratic FormulaQuadratic Formulaquadratic formula- derived by
completing the square.
aacbbx
242
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1-7 Quadratic Functions1-7 Quadratic Functionsa ≠ 0, is the set of points (x, y) that
satisfies the equation then this graph is a parabola
cbxaxy 2
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X and Y- InterceptX and Y- InterceptThe y-intercept of a parabola with
equation is c. If > 0, there are two x-
intercepts.If = 0, there is one x-intercept
(at a point where the parabola and the x-axis are tangent to each other).
If < 0, there are no x-intercepts.
cbxaxy 2
acb 42
acb 42
acb 42