Advanced MathVery hardValue at zero from vertex and one point
Advanced Math practice question
For the quadratic function f, the graph of y = f(x) in the xy-plane is a parabola with vertex (3, −5) that passes through (5, 3). What is the value of f(0)?
Answer: 13
f(x) = a(x − 3)² − 5. From f(5) = 3: 4a − 5 = 3, so a = 2. Then f(0) = 2(9) − 5 = 13.
Common wrong answers
- If you answered 4
- 4 uses a = 1 without checking the point (5, 3).
- If you answered 23
- 23 adds 5 instead of subtracting.
- If you answered -5
- −5 is the vertex's y-value, not f(0).
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