How are Quadratics and Nonlinear Functions tested on the SAT?

You solve quadratics by factoring, the quadratic formula, or completing the square; interpret vertex and factored forms; find a parabola's key features; and model exponential growth or decay.

Which form of a quadratic should I use?

Choose the form that matches the question: factored form reveals the roots, vertex form reveals the maximum or minimum, and standard form pairs with the quadratic formula or the discriminant.

What's the most common mistake on these questions?

Confusing the roots with the vertex, or losing a solution by dividing out a variable instead of setting the equation to zero. Always set a quadratic equal to zero before factoring or applying the formula.

SAT Math · Advanced Math

Quadratics and Nonlinear Functions

This skill spans quadratics and other nonlinear functions, including exponential models. You'll solve quadratic equations, interpret vertex and factored forms, and work with growth or decay. The strategic move is choosing the right form for the question: factored form reveals roots, vertex form reveals the maximum or minimum.

Quick answer

Quadratics and Nonlinear Functions is a digital SAT Math skill covering solving quadratics, interpreting their standard, factored, and vertex forms, and working with exponential growth and decay.

What it tests

Solving quadratics by factoring, the quadratic formula, or completing the square
Interpreting standard, factored, and vertex forms of a quadratic
Finding the vertex, axis of symmetry, and number of real solutions
Modeling and evaluating exponential growth and decay
Connecting a parabola's graph features to its equation

Common mistakes

Losing a solution by dividing out a variable instead of setting the equation to zero
Confusing the roots (from factored form) with the vertex (from vertex form)
Sign errors when applying the quadratic formula, especially under the square root
Treating exponential growth as if it were linear

How to improve

Pick the form that matches the question: factored for roots, vertex for max/min
Always set a quadratic equal to zero before factoring or applying the formula
Use the discriminant (b² − 4ac) to find the number of real solutions
Distinguish linear (constant difference) from exponential (constant ratio) patterns
Verify solutions by substituting them back into the original equation

Worked example

Solve: x² − 5x + 6 = 0.

Factor into (x − 2)(x − 3) = 0, so x = 2 or x = 3. Set each factor to zero because a product is zero only when one of its factors is zero. Check: 2² − 5(2) + 6 = 0 and 3² − 5(3) + 6 = 0.

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Related SAT Math skills

AlgebraLinear Equations and Systems AlgebraLinear Functions and Inequalities Advanced MathEquivalent Expressions Problem-Solving and Data AnalysisRatios, Rates, and Proportions

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Frequently asked questions

How are Quadratics and Nonlinear Functions tested on the SAT?: You solve quadratics by factoring, the quadratic formula, or completing the square; interpret vertex and factored forms; find a parabola's key features; and model exponential growth or decay.
Which form of a quadratic should I use?: Choose the form that matches the question: factored form reveals the roots, vertex form reveals the maximum or minimum, and standard form pairs with the quadratic formula or the discriminant.
What's the most common mistake on these questions?: Confusing the roots with the vertex, or losing a solution by dividing out a variable instead of setting the equation to zero. Always set a quadratic equal to zero before factoring or applying the formula.