Answer
$$f(x)=-2(x+3)^{2}−1$$
Work Step by Step
Standard form for any parabola is expressed as $f(x)=a(x−h)2+k$, where the point value $(h,k)$ represents the vertex point. The parabola in question, then, can be expressed as:
$f(x)=a(x−(−3))^{2}+(−1)=a(x+3)^{2}-1$
where the value of $a$ is currently unknown. To calculate it, one must simply plug in the point value $(-2,-3)$ given by the exercise:
$$f(-2)=-3=a((-2)+3)^{2}−1$$
$$-3 + 1=a(1)^{2}$$
$$-2 = a$$
The final expression in standard form comes to:
$$f(x)=-2(x+3)^{2}−1$$
