Advanced MathVery hardLeading coefficient from a vertex and a point
Advanced Math practice question
In the xy-plane, the parabola y = ax² + bx + c has its vertex at (3, −4) and passes through the point (1, 4). What is the value of a?
Answer: 2
In vertex form, y = a(x − 3)² − 4. Substituting (1, 4) gives 4 = 4a − 4, so a = 2.
Common wrong answers
- If you answered 1
- 1 uses 4 = 4a without the −4.
- If you answered 8
- 8 is 4a.
- If you answered -2
- −2 has the sign wrong; the parabola opens upward.
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