find a quadratic model for the set of values: (-2,-20), (0,-4), (4,-20)

Question

find a quadratic model for the set of values: (-2,-20), (0,-4), (4,-20)

 

 

Answer 1

y = ax²+bx+c

 

Since (0,-4) is on the curve, c = -4.

 

So, y = ax²+bx-4

 

Since (-2,-20) is on the graph, 4a - 2b - 4 = -20.  So, 4a - 2b = -16

 

Since (4,-20) is on the graph, 16a + 4b - 4 = -20.  So, 16a + 4b = -16

 

We have the system of equations:  4a - 2b = -16

                                                 16a + 4b = -16

 

Keep the second equation and multiply the first equation by 2 to get:

 

    8a - 4b = -32

  16a + 4b = -16

 

Adding the equations, we obtain 24a = -48.  So, a = -2

 

Since a = -2 and 4a - 2b = -16, -8 - 2b = -16

 

                                                   -2b = -8

 

                                                      b = 4

 

The quadratic equation is y = -2x² + 4x - 4.