Every rule the plots and drills lean on. One board, no guessing.
| Quadratic formula | x = −b ± √(b2 − 4ac)2a solves any quadratic set equal to zero. |
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| Discriminant | b2 − 4ac. Positive: two real roots. Zero: one. Negative: none real. |
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| Completing the square | Take half the middle coefficient, square it, add it to both sides. |
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| Function notation | f(x) is the machine’s output when x goes in. |
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| Domain and range | Domain is what may go in. Range is what can come out. |
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| Composition | f(g(x)): run the inner machine first, feed its output to the outer. |
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| Inverse functions | Swap x and y, then solve for y again. The inverse undoes the original. |
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| Rational exponents | A fraction in the exponent names a root: the bottom is the root, the top is the power. |
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| Simplifying radicals | Pull every perfect square out from under the root sign. |
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| Imaginary unit | i2 = −1. The unit that opens the complex numbers. |
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| Logarithm | logb x asks: b to what power gives x? |
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| Exponential growth | y = abx. A base above one grows; below one, it decays. |
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| Circle equation | x2 + y2 = r2, centered at the origin. |
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| Arithmetic sequence | Add the same difference at every step. |
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| Geometric sequence | Multiply by the same ratio at every step. |
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| Systems of three | Eliminate one letter to get two equations, then eliminate again. |
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