16Hit1600
Advanced MathVery hardFinding a parameter from a graph's behaviour

Advanced Math practice question

The graph of f(x) = ax² + 8x + c in the xy-plane has its vertex at (2, 11). What is the value of a?

Answer: -2 or −2

The vertex's x-coordinate is −b/(2a) = −8/(2a) = 2, so 2a = −4 and a = −2. (Then c = 3, since f(2) = −8 + 16 + c = 11.)

Common wrong answers

If you answered 2
2 has the wrong sign; −8/(2a) = 2 gives a negative a.
If you answered 3
3 is c, not a.
If you answered -4
−4 forgets the 2 in the denominator: −8/(2a), not −8/a.

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