SAT Math: Completing the Square
28+ practice questions in Praczo
The concept, explained
- 1
Completing the square rewrites ax² + bx + c in vertex form a(x − h)² + k, revealing the vertex directly.
- 2
Step 1: if a ≠ 1, factor it out from the x-terms. Step 2: take half of the b-coefficient, square it, add and subtract inside the expression.
- 3
The vertex is (h, k). This method also allows you to solve quadratics that do not factor neatly.
- 4
The SAT often gives a quadratic in standard form and asks for the vertex or minimum/maximum value — completing the square is the direct route.
- 5
After completing the square, the solutions are x = h ± √(−k/a) (if solving for roots).
- ✗ Forgetting to both add AND subtract the square inside the expression — you must keep the equation balanced.
- ✗ Not dividing by a first when a ≠ 1 before completing the square, which distorts the result.
SAT-style practice
Which of the following is equivalent to x² − 6x + 5?
Ready to master this concept?
Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.
3-day free trial — no credit card required