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12 multiple-choice questions and 38 flashcards on Quadratic Functions and Complex Numbers, about 8% of the High School Algebra 2 bank. Every one carries a written rationale.
Quadratic Functions and Complex Numbers is one of 9 chapters in CoStudy's High School Algebra 2 bank, and it holds 12 of the bank's 150 multiple-choice questions — roughly 8% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
3 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
Equation of a circle with center (−3, 4) and radius 5:
Answer: C — (x + 3)² + (y − 4)² = 25
Standard form (x − h)² + (y − k)² = r². Center (−3, 4): h = −3 → (x − (−3))² = (x + 3)². Radius squared = 25. A) Sign error on center coordinates. B) Used radius not radius². D) Both errors.
What is the value of i² where i is the imaginary unit?
Answer: D — -1 (by definition: i = √(-1), so i² = -1)
Imaginary unit: i = √(-1). Therefore i² = -1. Powers cycle: i¹=i, i²=-1, i³=-i, i⁴=1, then repeats. Foundation of complex numbers.
Compute (1 + 2i)(3 − i).
Answer: C — 5 + 5i
FOIL: 3 − i + 6i − 2i² = 3 + 5i − 2(−1) = 5 + 5i. A) Forgot the i² conversion entirely. B) Real-part error. D) Did not simplify i² = −1 (half-right).
4 cards from the 38 in this chapter.
Multiply: (x − 3)(x + 3).
x² − 9. (Difference of squares.)
What's the standard form of a quadratic?
ax² + bx + c = 0.
Multiply: (2x + 3)(x − 4).
2x² − 5x − 12.
What is 'completing the square'?
Method to rewrite ax² + bx + c as a(x − h)² + k. Useful for solving and graphing.
These are a sample. The full Quadratic Functions and Complex Numbers chapter runs 50 items with per-chapter progress tracking, on the web and in the iOS app.
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