Answer
a) $x = -2$
b) $x = 3, -7$
c) $x = 0, -4$
d) see graph
Work Step by Step
$f(x) = x^2 + 4x - 21$
$a = 2$, $b = 4$ $c = -21$
a) Vertex of f(x)
$x = \frac{-b}{2a} = -2$
b)x-intercepts
Solution $f(x) = 0$ will give x-intercepts
$\Rightarrow x^2 + 4x - 21 = 0$
$\Rightarrow (x-3)(x+7) = 0$
$\Rightarrow x = 3, -7$
c)
$f(x) = -21$
$\Rightarrow x^2 + 4x - 21 = -21$
$\Rightarrow x(x+4) = 0$
$\Rightarrow x = 0, -4$