Yes, that school is accredited and the diploma is equal to a diploma from a brick-and-mortar high school diploma.

If you have the SAT/ACT scores and meet the entrance requirements of the school of your choice, you can attend any College or University in Texas.

Homeschool graduates are specifically protected by law from discrimination by Texas colleges: “Because the State of Texas considers successful completion of a nontraditional secondary education to be equivalent to graduation from a public high school, an institution of higher education must treat an applicant for admission to the institution as an undergraduate student who presents evidence that the person has successfully completed a nontraditional secondary education according to the same general standards as other applicants for undergraduate admission who have graduated from a public high school.” Tex. Educ. Code Ann. § 51.9241.**

Unfortunately, it seems as though Continental Academy had last its accreditation back in 2009. If colleges won’t accept a diploma from the institution, perhaps you can take the ged (general equivalency diploma).