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Equivalent expressions
Factoring polynomials, expanding, combining like terms, and working with rational expressions.
Nonlinear equations in one variable
Solving quadratic, polynomial, and rational equations. Using the discriminant to classify solutions.
Systems with a linear and nonlinear equation
Solving systems where one equation is linear and one is quadratic or another curve.
Nonlinear functions
Interpreting quadratic, exponential, and radical functions from equations, tables, and graphs.
Function notation and transformations
Evaluating f(x), g(f(x)), and identifying the effect of a, h, k on f(x) = a·f(x−h)+k.
主要公式
x = (−b ± √(b² − 4ac)) / 2a (quadratic formula)y = a(x − h)² + k (vertex form)D = b² − 4ac (discriminant)a² − b² = (a+b)(a−b) (difference of squares)(a ± b)² = a² ± 2ab + b² (perfect square)f(t) = a · bᵗ (exponential growth/decay)試験対策のヒント
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Factor first — most quadratics on the SAT factor cleanly without needing the formula.
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The discriminant tells you how many real solutions exist before you solve.
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Vertex form is fastest for finding the maximum or minimum value.
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For exponential functions, b > 1 means growth; 0 < b < 1 means decay.