How do I solve this?

Question

Which kind of function best models the data?Write an equation to model the data.

1. (-4,-32),(-2,-8),(0,0),(2,-8),(4,-32)

 

 

Answer 1

Michael is correct...the graph is a parabola that opens downward, so it points upward.  I figured out that the equation for these set of points is y = -2x² .  

 

Answer 2

If you plot the points, it's obvious that this is a parabola with vertex at (0, 0).

Thus, it is of the form y = ax^2.  

As it contains the point (2, -8), substituting, -8 = a * 2^2

Thus, -8 = 4 a 

a = -8/4 = -2

Note that this works for the other 4 points:

(-4, -32)   -32 = -2 * (-4)^2

(-2, -8)     -8 = -2 * (-2)^2

(0, 0)         0 = -2 * 0^2

(4, -32)      -32 = -2 * 4^2

 

Answer 3

As you can see, the y values are symmetrical to each other as x increases.  This happens in a parabola.  The turning point is (0, 0).  The y values increase, then decrease.  This is a parabola opening downward.