Why a textbook? Because it is good for students to learn to use regular textbooks. It helps prepare them for any further studies (whether college or vocational) where they need to learn on their own, reading a textbook.
Also, good textbooks include not only basic exercises but also challenging ones. If you decide to go with some online curriculum or video instruction, a regular textbook can act as a reference and as an additional problem "bank" for those challenging problems. You can also use it to check that your student is really getting all the instruction that is present in a typical high school math course.
Why videos? Because those replace the component that is present in a regular classroom: the teacher explaining concepts and ideas. Learning algebra or geometry from a textbook alone might be too difficult for some students. If the parent cannot explain the math, videos will help bridge the gap. In today's world, there exist MANY free websites with math videos that can be used. And, some companies provide videos tailored to a specific textbook.
(Please note: Math Mammoth users can start high school math directly after finishing Math Mammoth grade 7, since MM7 is a prealgebra program. There is no need to use a separate math program for grade 8.)
I have written a comprehensive article explaining the basic options for algebra 1 course in a homeschool setting and detailed descriptions of some textbooks. The article also lists free algebra video websites, online curricula, and gives a link to a list of algebra tutorial websites.
Recommendations for algebra 1 curriculum
I have not seen very many geometry courses, but I have personally reviewed two high school geometry textbooks that I can recommend:
I have also heard (and based on the samples it seems so) that Teaching Textbooks Geometry is a decent curriculum. It is probably easier than the two textbooks mentioned above. Keep in mind though that in general, their gradelevel curriculum is very easy, 12 grade levels behind Math Mammoth, and does not provide good word problems that would enable students to learn problem solving.
Some companies that provide videos and other helps to match regular high school textbooks are:
No matter which curriculum you use, you can use free teaching videos by various people. These websites offer free videos online for high school math courses.
cK12
CK12 is a large, free site for learning and practicing math and science. It contains textbased lessons, FlexBooks® (digital textbooks in PDF, ePub and mobi formats), videos, and quizzes for multitudes of math and science topics from K to grade 12.
Khan Academy
Possibly the web's biggest and free site for math videos. What started out as Sal making a few algebra videos for his cousins has grown to over 2,100 videos and 100 selfpaced exercises and assessments covering everything from arithmetic to physics, finance, and history.
LearnZillion
Free math videos for all topics in K8. The videos are organized according to the Common Core Standards (CCS), but can be used even if you don't follow the CCS — just follow the lesson titles by topics.
MathTV.com
Over 6,000 free, online video lessons for basic math, algebra, trigonometry, and calculus. Videos also available in Spanish. Also includes online textbooks. I've written a review of MathTV.
HippoCampus
Online interactive lessons (free) covering high school algebra and calculus courses (including AP calculus).
BrightStorm Math
Over 2,000 free videos covering all high school math topics from algebra to calculus. Registration required (free).
MathVids.com
Free math videos grouped by math topic. Basic math, middle school, high school, and college levels. Also includes links to further resources.
Algebra Within Reach
Free algebra videos presented by Dana Mosely, workedout solutions for selected exercises, and other companion helps for Ron Larson's algebra textbooks.
Virtual Nerd
Video tutorials for prealgebra, algebra 1, algebra 2, and intro physics. This will also include practice problems and quizzes sometime during 20102011 school year. Includes both a free and paid (premium) versions.
Math Ops
Free online prealgebra and algebra course that includes stepbystep narrated tutorials, videos, and online quizzes.
HSTutorials.net
Free animated and narrated math tutorials  prealgebra, algebra 1, geometry.
LearnersTV.com
Free video lectures, audio lectures, notes, and ebooks etc. for high school and college level math. Also has material for other sciences.
Sophia
A large online library of short video lessons and quizzes covering courses from prealgebra through calculus. The videos are recorded by several different tutors, who vary in their methods and teaching styles, so you have the chance to learn the same lesson from several perspectives.
Holt Online Learning
This site includes online video lessons and other support materials to accompany Holt high school math textbooks. Click on a course, then choose the Homework help, choose a chapter, and then view the lessons.
Jooble
Not a curriculum or video website  but Jooble allows you to search for jobs (in the USA), whether you're in high school or beyond.
Hope this helps!
Maria Miller
Math Mammoth TourConfused about the different options? Take a virtual email tour around Math Mammoth! You'll receive: An initial email to download your GIFT of over 400 free worksheets and sample pages from my books. Six other "TOURSTOP" emails that explain the important things and commonly asked questions concerning Math Mammoth curriculum. (Find out the differences between all these differentcolored series!)This way, you'll have time to digest the information over one or two weeks, plus an opportunity to ask me personally about the curriculum. A monthly collection of math teaching tips & Math Mammoth updates (unsubscribe any time) We respect your email privacy.
Note: You will FIRST get an email that asks you to confirm your email address. If you cannot find this confirmation email, please check your SPAM/JUNK folder. 
"Mini" Math Teaching CourseThis is a little "virtual" 2week course, where you will receive emails on important topics on teaching math, including:
 How to help a student who is behind You will also receive: A GIFT of over 400 free worksheets and sample pages from my books right in the very beginning. A monthly collection of math teaching tips & Math Mammoth updates (unsubscribe any time)We respect your email privacy.
Note: You will FIRST get an email that asks you to confirm your email address. If you cannot find this confirmation email, please check your SPAM/JUNK folder. 
Maria's Math TipsEnter your email to receive math teaching tips, resources, Math Mammoth news & sales, humor, and more! I tend to send out these tips about once monthly, near the beginning of the month, but occasionally you may hear from me twice per month (and sometimes less often). Peek at the previous tips here. You will also receive:
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