16Hit1600
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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