Final answer:
To find the quadratic equation that includes the points (2,3), (3,15), and (5,63), we set up a system of equations based on the quadratic formula y = ax^2 + bx + c, then solve for constants a, b, and c.
Step-by-step explanation:
To write a quadratic equation that contains the points (2,3), (3,15), and (5,63), we will assume that the equation is of the form y = ax^2 + bx + c, where a, b, and c are constants. Substituting each given point into this equation, we will obtain three equations as follows:
- 3 = 4a + 2b + c
- 15 = 9a + 3b + c
- 63 = 25a + 5b + c
We can solve these equations simultaneously to find the values of a, b, and c that will make the equation valid for all three given points. This system of equations can be solved via methods such as substitution, elimination, or matrix methods to find the values of a, b, and c. Once these constants are determined, the quadratic equation can be written in the form y = ax^2 + bx + c.