Put the coordinates of the points (1, 21) and (2, 6) to the equation of the function:
[tex]y=a(x+1)^2+k\\\\(1,\ 21)\\\\21=a(1+1)^2+k\\21=a(2)^2+k\\21=4a+k\qquad\text{subtract 4a from both sides}\\21-4a=k\qquad(*)\\\\(2,\ 6)\\\\6=a(2+1)^2+k\\6=a(3)^2+k\\6=9a+k\qquad(**)[/tex]
Substitute (*) to (**):
[tex]6=9a+(21-4a)\\6=9a+21-4a\\6=5a+21\qquad\text{subtract 21 from both sides}\\-15=5a\qquad\text{divide both sides by 5}\\-3=a\to\boxed{a=-3}[/tex]
Put the value of a to (*):
[tex]k=21-4(-3)\\k=21+12\\\boxed{k=33}[/tex]
Answer:
[tex]y=-3(x+1)^2+33[/tex]
