What an equation for (-1,-1) (0,-3) (1,-1)

Question

What’s the anwser

Answer 1

Plotting the points, we see that the points don't lie on a line.

 

However, three points that don't lie on a line determine a parabola.

 

  y = Ax² + Bx + C

 

Since (0, -3) is on the graph, C = -3.

 

So, y = Ax² + Bx - 3

 

Since (-1,-1) is on the graph, A - B - 3 = -1.  So, A - B = 2

 

Since (1,-1) is on the graph, A + B - 3 = -1.   So, A + B = 2

 

We have the system of equations:  A - B = 2

                                                   A + B = 2

 

Add the equations to get 2A = 4.   Therefore, A = 2

 

Since A = 2 and A + B = 2, B = 0.

 

The three given points lie on the graph of y = 2x² - 3.