Quadratic equations appear on every SAT. You will see 2-4 questions per test. The key is knowing which method to use and when.

The 4 Methods

Method 1: Factoring

Use when: The quadratic factors easily (leading coefficient is 1 or the factors are obvious).

Solve :

Factor:

Solutions: or

Speed tip: If , find two numbers that multiply to and add to .

Method 2: Square Root Method

Use when: The equation has no middle term, like or .

Solve :


Method 3: Completing the Square

Use when: The SAT explicitly asks for vertex form, or you need to find the vertex.

Solve :




Method 4: Quadratic Formula

Use when: Nothing else works, or the coefficients are messy.

Solve :

or

The Discriminant Shortcut

The discriminant tells you the number of solutions WITHOUT solving:

The SAT loves asking "how many solutions does this equation have?" — just compute the discriminant.

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Common Mistakes to Avoid

  • Forgetting the : gives AND , not just .
  • Dividing by : Never divide both sides by — you lose the solution. Factor instead.
  • Sign errors in the quadratic formula: The formula has , not . If , then .
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SAT Pro Tip

Before using the quadratic formula, always check if the expression factors. Factoring takes 10 seconds; the quadratic formula takes 45+ seconds. On the SAT, time saved is points earned.

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