please help

Find the equation of the parabola that goes through the three points (0, 9), (1, 7) and (2, 7).

Hello Guest!

$y=ax^2+bx+c$

Put the coordinates of the three points in
the equation $y=ax^2+bx+c$, and solve for a, b, and c.

I.    $9=c$

II.   $7=a+b+9$

III.  $7=4a+2b+9$

4 * II  .     $28=4a+4b+36$

  - III.         $\underline{7=4a+2b+9}$

                21  =           2b  + 27 

$2b=21-27=-6$

$b=-3$

$7=a+b+9$

$7=a-3+9$

$a=1$

The general equation  $y=ax^2+bx+c$

becomes the real equation $y=x^2-3x+9$.

  !