Answer:
[tex](-\infty, -3)[/tex] (the interval over which [tex]x < -3[/tex].)
Step-by-step explanation:
The expression [tex]\text{$y = a\, (x - h)^{2} + k$, $a \ne 0$}[/tex] is the vertex form equation of a parabola with vertex [tex](h,\, k)[/tex]. This parabola opens upwards if [tex]a > 0[/tex] and downwards otherwise.
Rewrite the expression of [tex]f(x)[/tex] in this question to fit the vertex form equation above:
[tex]\begin{aligned}f(x) &= 2\, (x + 3)^{2} - 5 \\ &= 2\, (x - (-3))^{2} - 5\end{aligned}[/tex].
Compare this expression to the vertex form equation. The vertex of this parabola would be [tex](-3.\. -5)[/tex], and the parabola would open upwards since [tex]a = 2[/tex]is greater than [tex]0[/tex].
A parabola that opens upwards is decreasing to the left of the vertex and increasing to the right of the vertex. Thus, the [tex]f(x)[/tex] in this question would be decreasing for all points with [tex]x < -3[/tex] (to the left of the vertex.) That would correspond to the interval [tex](-\infty,\, -3)[/tex].
