Linear And Quadratic Functions
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4Algebra III
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Semester I Outline
Chapters 1 – 5
Chapter 1: Linear and Quadratic Functions
Section 1.1: Points and Lines
• Solving systems of equations algebraically
o Solution is a coordinate (point of intersection)
o Solve by canceling variables
• Distance formula
• Midpoint formula
Section 1.2: Slopes of Lines
• Slope Formula (change in y over the change in x)
• Parallel lines: same slope
• Perpendicular lines: opposite reciprocals
Section 1.3: Finding an equation of a line
• General or Standard Form Ax + By = C
o A, B, and C are integers and A is positive
• Slope-intercept Form
• Point-Slope Form
• Intercept Form
• Know how to find a perpendicular bisector
Section 1.4: Linear Functions and Models
• Evaluating functions ex: If f(x) = 2x + 1 find f(2)
• Finding zeros of a function by setting the equation equal to zero
Section 1.5: The Complex Numbers
2
and
i = −
1
i = −
1
•
• Imaginary number a + bi (a is the real part and b is the imaginary part)
• If a + bi is a root so is a – bi
Section 1.6: Solving Quadratic Equations
• The root, or solution, is where the graph crosses the x-axis
• Methods: Factoring, Completing the Square, and Quadratic Formula
o Try to factor first
o If not factorable then use the Quadratic Formula
• Discriminant (2 imaginary roots, 2 real roots, or 1 real root)
Section 1.7: Quadratic Functions and their Graphs
Section 1.8: Quadratic Models
• Opening up or down
• Ex: Given f(0) = 5, f(1) = 10 and
• Axis of Symmetry
f(2) = 19, find a quadratic function
• Vertex
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