Find the quadratic function y=ax^2 +bx+c whose graph passes through the given points.

Question

(1,5),(-1,11),(2,14)

Answer 1

We can create a system of 3 equations with 3 unknowns

 

y = ax^2 +bx + c      At each point we have and x and a y

 

let's look at (1,5)

 

5 = a(1)^2 +b(1) + c

 

5 = a + b + c            This tells me the sum of the coefficients = 5

 

now for the other 2 points

 

11 = a -b + c

 

14 = 4a +2b + c

 

Now solve this 3X3 system

 

 

11 = a -b + c

14 = 4a +2b + c

 

5 = a + b + c

 

If you need help on solving the system, please reply