All SAT GuidesPractice Nonlinear Functions & Quadratic Equations questions
Study Guide
Nonlinear Functions & Quadratic Equations
This topic covers parabolas, exponential functions, and other nonlinear relationships. You must be able to interpret graphs, identify key features, and solve related equations.
Key Rules
- Parabola vertex form: f(x) = a(x-h)² + k, vertex at (h, k). If a > 0, opens up; if a < 0, opens down.
- Exponential functions: f(x) = a·bˣ. If b > 1, growth. If 0 < b < 1, decay.
- x-intercepts of a parabola = solutions to the quadratic equation f(x) = 0.
- The axis of symmetry of a parabola is x = -b/(2a) in standard form.
Common Mistakes to Avoid
- Confusing vertex (h, k) with x and y intercepts.
- Thinking f(x) = a(x-h)² + k has vertex at (-h, k) — the sign convention is tricky.
- Confusing exponential growth (bˣ) with polynomial growth (xⁿ).
- Misreading graphs: the y-intercept is at x=0, not where the curve appears to start.
SAT Strategy Tips
- →To find vertex from standard form: x-coordinate = -b/(2a), then plug in to find y.
- →From vertex form f(x) = a(x-h)² + k: vertex is literally (h, k).
- →The SAT loves asking about the effect of changing a, h, or k on the graph.
- →For exponential: a is the initial value (y-intercept when x=0); b is the multiplier per unit.
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