Question

Can someone please use these coordinates to write the equation of a quadratic function that models the data. The coordinates are. (0,0) (2,5) (5,7)

Answer 1

Try this option:

1. the rule: common view of the equation of the quadratic function is 'y=ax²+bx+c', where a, b and c - numbers.

2. if to substitute the given coordinates into  common equation, it is possible to write 3 equations: (for (0;0)) c=0; (for (2;5)) 4a+2b+c=5; (for (5;7)) 25a+5b+c=7.

3. for the system of the linear equations:

$\left \{ \begin{array}{ccc}c=0\\4a+2b+c=5\\25a+5b+c=7\end{array}\right => \ \left \{ \begin{array}{ccc}c=0\\b=97/30\\a=-11/30\end{array}\right$

4. Answer:

$y= -\frac{11x^2}{30} +\frac{97x}{30}$