Question

Hellppppp!!!!

Write the equation of a quadratic function that contains the points (1,21), (2,18), and (-1,9).

Answer 1

`y=-3x^(2) +6x+18`

Explanation:

`y=ax^(2) +bx+c`

Substitute the three points we have.

`21=a+b+c\\18=4a+2b+c\\9=a-b+c\\`

Take the first less the third.

`2b=12\\b=6`

`15=a+c\\6=4a+c\\15=a+c\\`

Take the second and subtract the first.

`-9=3a\\a=-3`

Therefore, we can calculate c.

`c=18.`

Therefore, our equation is
`y=-3x^(2) +6x+18`