16Hit1600
Advanced MathVery hardLeading coefficient from zeros and a maximum value

Advanced Math practice question

A quadratic function f has zeros at x = 2 and x = 8, and its maximum value is 9. What is the leading coefficient of f?

Answer: -1

f(x) = a(x − 2)(x − 8), with its maximum at the axis x = 5: f(5) = a(3)(−3) = −9a = 9, so a = −1.

Common wrong answers

If you answered 1
1 would give a minimum of −9, not a maximum of 9.
If you answered 9
9 is the maximum value, not the coefficient.
If you answered -9
−9 forgets to divide by (3)(−3).

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