intermediate

Quadratic,Linear, Exponential Function

Comprehensive AI-generated study curriculum with 3 detailed note modules.

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Course Syllabus

  1. Foundations of Functions
  2. Linear Functions and Equations
  3. Quadratic Functions: Forms and Graphs
  4. Solving Quadratic Equations and Applications
  5. Exponential Functions and Growth/Decay
  6. Comparing and Contrasting Functions

Study Notes

Exponential Functions and Growth/Decay

  • y is the final amount.
  • a is the initial amount (what you start with when x = 0).
  • b is the growth/decay factor. This is the multiplier for each unit of x.
  • x is often time or the number of periods.

The value of b tells you everything:
* If b > 1, you have exponential growth. The quantity is increasing.
* If 0 < b < 1, you have exponential decay. The quantity is decreasing.
* b cannot be 1 (because 1^x is always 1, which is just a constant line) and cannot be negative (it would jump between positive and negative values oddly).

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Solving Quadratic Equations and Applications

A quadratic equation is any equation that can be rearranged into the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are numbers, and $a
eq 0$. The solutions (also called roots or zeros) are the values of $x$ that make the equation true. There can be zero, one, or two real solutions.

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