No. Expenses paid to attend high school do not qualify for the education credits because a high school is not an eligible educational institution. An eligible educational institution is any college, university, vocational school, or other post-secondary educational institution eligible to participate in a student aid program administered by the Department of Education. It includes virtually all accredited, public, nonprofit, and proprietary (privately owned profit making) post-secondary institutions.

References:

• Publication 970, Tax Benefits for Education
• Tax Topic 605, Education Credits
• Form 8863 (PDF), Education Credits (Hope and Lifetime Learning Credits)

Source: www.irs.gov