Answer:
[tex]y=-3x^{2} +6x+18[/tex]
Step-by-step explanation:
[tex]y=ax^{2} +bx+c[/tex]
Substitute the three points we have.
[tex]21=a+b+c\\18=4a+2b+c\\9=a-b+c\\[/tex]
Take the first less the third.
[tex]2b=12\\b=6[/tex]
[tex]15=a+c\\6=4a+c\\15=a+c\\[/tex]
Take the second and subtract the first.
[tex]-9=3a\\a=-3[/tex]
Therefore, we can calculate c.
[tex]c=18.[/tex]
Therefore, our equation is [tex]y=-3x^{2} +6x+18[/tex]
