16Hit1600
Advanced MathVery hardLeading coefficient from three values of a quadratic

Advanced Math practice question

The function f is defined by f(x) = a(x − h)² + k, where a, h, and k are constants. If f(0) = f(6) = 3 and f(3) = −6, what is the value of a?

Answer: 1

f(0) = f(6) puts the axis at x = 3, so h = 3 and k = f(3) = −6. Then f(0) = 9a − 6 = 3, so a = 1.

Common wrong answers

If you answered 3
3 is h, not a.
If you answered -1
−1 gives f(0) = −15.
If you answered -6
−6 is k, not a.

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