Day 2 - Section 1: Notation and Quadratics

Key Topics

• Different Notations
• Quadratic Functions
• Domain and Range
• Interval Notation
• Set Builder Notation
• Graphing Linear Equations

Quadratic Functions

• Example 6: Quadratic
  • Quadratic functions are u-shaped and can be upside down.
  • Domain for quadratics: All real numbers, or (-∞, ∞).

Interval Notation

• Uses parentheses to denote values not included.
• Use brackets for solid dots and parentheses for open dots.
• Negative/positive infinity uses parentheses.

Set Builder Notation

• Utilizes less than and greater than symbols.
• Writing: "All x such that x is less than 2" (without equal sign for open dots).
• Often corresponds with number lines from Algebra 1.

Domain and Range

• Quadratic domain: (-∞, ∞)
• Example of determining domain and range for a specific function:
  • Identify smallest/largest value on the y-axis for the range.
  • Example values for y: Greater than or equal to -6.
  • Range can go to infinity if the graph opens upwards.

Three Ways to Write

1. Words: Specify the domain/range using language.
2. Interval Notation: Use (, ) or [, ] to show intervals.
3. Set Builder Notation: Use symbols and inequalities.

Graphing Linear Equations

• Slope-Intercept Form (y = mx + b)
  • m: Slope
  • b: y-intercept
• Steps to Graph:
  1. Plot the y-intercept.
  2. Use the slope to find another point.
  3. Draw the line through the points.
• Special Cases:
  • No y-intercept: Start at origin (0,0).
  • Horizontal line when slope = 0.

Special Cases

• Piecewise Functions:
  • Graphs can include segments with open or closed circles.
  • Use union symbol (U) for multiple segments.
  • Determine constraints from graph segments.

Homework/Practice

• Apply graphing techniques to y = mx + b problems.
• Practice determining domain and range using different notations.

Additional Notes

• Interval Notation: Always list intervals smallest to largest.
• Lines: Almost all have domain/range as all real numbers, except vertical/horizontal lines.

Study Tips

• Review Concepts: Try rewriting examples using different notations.
• Graphing Practice: Work on graphing various forms of linear equations.

Note: This lecture was recorded for review, and notes are available for reference. Review the video if needed to reinforce understanding.