WAEC 2016 · Paper 2 · Q2

Functions

(a)
A function $f$ is defined on the set $\mathbb R$ of real numbers by $f : x \to mx^2 + nx + 2$ , where $m$ and $n$ are constants. If $f(-2) = 0$ and $f(1) = 3$ , find the values of $m$ and $n$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

$f(-2) = 0$ : $m(-2)^2 + n(-2) + 2 = 0$ , so $4m - 2n + 2 = 0$ .
Divide by 2: $2m - n = -1$ .
$f(1) = 3$ : $m + n + 2 = 3$ , so $m + n = 1$ .
Add the two equations: $3m = 0$ , so $m = 0$ .
Then $n = 1 - 0 = 1$ .
Check: $f(x) = x + 2$ gives $f(-2) = 0$ ✓ and $f(1) = 3$ ✓.

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