Question

Use the inverse matrix method to write the equation of the quadratic y=ax^2 + bx+ c that contains the points of (4,8),(0,12), and (7,-16)

Answer 1

9514 1404 393

Answer:

y = -x^2 +3x +12

Explanation:

The matrix equation will have x^2, x, and 1 as the coefficients of the variables a, b, c in each row.

`\left[\begin{array}{ccc}16&4&1\\0&0&1\\49&7&1\end{array}\right]\cdot\left[\begin{array}{c}a\\b\\c\end{array}\right]=\left[\begin{array}{c}8\\12\\-16\end{array}\right]`

The inverse of the coefficient matrix can be calculated using any of a number of web tools or calculators. The solution using the inverse matrix method is ...

`\left[\begin{array}{ccc}-(1)/(12)&(1)/(28)&(1)/(21)\\\\(7)/(12)&-(11)/(28)&-(4)/(21)\\\\0&1&0\end{array}\right]\cdot\left[\begin{array}{c}8\\12\\-16\end{array}\right]=\left[\begin{array}{c}-1\\3\\12\end{array}\right]`

The equation is ...

y = -x^2 +3x +12