How to find a quadratic function whose vertex is at the point (2,9) and has the given x intercepts (1,0) &amp; (3,0)?

Question

How to find a quadratic function whose vertex is at the point (2,9) and has the given x intercepts (1,0) &amp;amp; (3,0)?

chaghirun · Accepted Answer

Every quadratic function can be expressed in the standard form            f              (        x        )              =    a          x      2        +    b    x    +    c  In many Algebra textbooks, the preceding problem is rewritten using factoring and completing the square:            f              (        x        )              =    a                  (        x        -        h        )            2        +    k  , where             (      h      ,      k      )       is the vertex.Because       h    =    2   and       k    =    9  , we can plug these into the rewritten             f              (        x        )             to get:             f              (        x        )              =    a                  (        x        -        2        )            2        +    9  The roots let us solve for       a  . The first root says             f              (        1        )              =    0   and the second root says             f              (        3        )              =    0  . Thus,             f              (        1        )              =    a                  (        1        -        2        )            2        +    9    =    0   This gives       a    =    -    9              f              (        3        )              =    a                  (        3        -        2        )            2        +    9    =    0  . This also gives       a    =    -    9  Hence             f              (        x        )              =    -    9                  (        x        -        2        )            2        +    9  . To get the standard form, factor it out and make it simpler:            f              (        x        )              =    -    9          x      2        +    36    x    -    27

How to find a quadratic function whose vertex is at the point (2,9) and has the given x intercepts (1,0) & (3,0)?

Answered question

Answer & Explanation

New Questions in Algebra I