Answer
$(-3,3)$
Work Step by Step
We are given the inequality:
$x^2-9<0$
$f(x)=x^2-9$
Determine the intercepts:
$y$-intercept: $f(0)=0^2-9=-9$
$x$-intercepts: $x^2-9=0$
$(x+3)(x-3)=0$
$x+3=0$ or $x-3=0$
$x=-3$ or $x=3$
The $y$-intercept is -9; the $x$-intercepts are -3 and 3.
Determine the vertex:
$x_V=-\dfrac{b}{2a}=-\dfrac{0}{2(1)}=0$
$y_V=f(x_V)=0^2-9=-9$
The vertex is $V(0,-9)$.
Graph the function.
The graph is below the $x$-axis for:
$-3
