HK, as always, makes important points. One thing that I should've mentioned originally, but that the OP seemed to anticipate, is that there are two divisions of the school. One is "regular" Laurel Springs, which is better than but roughly analogous to K12 (based on my experience, LSS has, more often, in-house curriculum and "real" teachers you can talk to; K12 not so much; caveat that I haven't seen K12 for several years). Even "regular" Laurel Springs is light years better than Apex (from what I've seen). I can't speak to Connections; I've never seen its curricula or had a child enrolled in it.
The other division is the Laurel Springs Academy for the Gifted and Talented, which requires testing and recommendations to document giftedness and has separate teachers, students, symposia, and so on. The peers seem quite good but aren't all that visible to us, outside of the symposia and some clubs. Instead, the big difference is that the Academy students are able to request 100% customization. So if you want to replace the content of a course with something higher-level that is academically justified as MORE rigorous, you can do it.
Customization is the critical safety valve that I have not seen at any other online provider: I am not boxed in if I'm dissatisfied with course content. Teachers often have good ideas on their own for customization, because they do have experience with other gifties, but they're open to a well-reasoned argument for customization from parents, as long as the rigor is there.
Hope that helps. Whether it's worth the money and the obligation to meet the CA graduation requirements is an individual decision. I wouldn't use any of the other online providers. DC was accepted at Stanford University Online High School, but at that time the school had a very disorganized vibe and onerous administrative rules and penalties (you have to "show up" live twice a week; are penalized if you don't; and are penalized if your computer/software etc. isn't working; all this scared my DC, who has many outside activities not entirely under our scheduling control). We like the at-your-own pace of homeschooling, so Laurel Springs works for us. Again, others may have different needs, and of course "real" homeschooling is most flexible.
Whether the math is good probably depends on your home teacher. The textbooks are all standard California texts from major publishers and not Everyday Math (thank God). I've found that there are options within Laurel Springs-- if you want, say, the Lial instead of something else, you can do it. But what I'm seeing is that the standard textbooks themselves seem to take a fairly mechanical and non-theoretical approach. So if teaching the textbook is what your parent or tutor provides, that's what you'll get. We do more than that, but that's us. I haven't had a HS kid before, so whether this is Common Core-related or just American education, I do not know.
A downside: the Gifted & Talented Academy is an all-or-nothing proposition, so, bluemagic, the only option for a single course is "regular" Laurel Springs.
