SAT Math · Passport to Advanced Math
Quadratic functions and equations
Solving, factoring, vertex form, and parabolic models.
What's tested in this subtopic
Items here ask you to solve a quadratic equation by factoring, completing the square, or the quadratic formula; to identify the vertex of a parabola from standard or vertex form; or to interpret the meaning of the vertex, axis of symmetry, or zeros in a real-world context (projectile height, profit, revenue).
Tactics that actually move your score
When solving, try factoring first — if the leading coefficient is 1 and the constant has clean factor pairs, you can usually factor in your head in under ten seconds. Otherwise reach for the quadratic formula. To find the vertex from standard form, use x = −b/(2a). For projectile or profit problems, recognize that the vertex is the maximum or minimum and the question almost always asks for it. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy What is the sum of the solutions to the equation x² + 11x + 30 = 0?
- Easy What is the sum of the solutions to the equation x² + 2x = 0?
- Medium What is the sum of the solutions to the equation x² − 49 = 0?
- Medium What is the sum of the solutions to the equation x² − 11x + 30 = 0?
- Medium What is the sum of the solutions to the equation x² + 2x − 3 = 0?
- Hard What is the sum of the solutions to the equation x² − 1 = 0?
- Easy What is the sum of the solutions to the equation x² − 16 = 0?
- Easy What is the sum of the solutions to the equation x² − 16 = 0?
- Medium What is the sum of the solutions to the equation x² − 7x + 12 = 0?
- Medium What is the sum of the solutions to the equation x² + 3x − 4 = 0?
- Medium What is the sum of the solutions to the equation x² + 3x + 2 = 0?
- Hard What is the sum of the solutions to the equation x² + 1x − 12 = 0?
- Easy What is the sum of the solutions to the equation x² + 3x + 2 = 0?
- Easy What is the sum of the solutions to the equation x² − 5x + 6 = 0?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.