Question

Which type of function best models the data in the table? Justify your choice.

Answer 1

Answer:

Quadratic equation:  $y=-2x^2+32x+22$

Explanation:

We need to find best model of given data in the table.

1) Linear: For linear slope of the line must be same. Slope is change in y over change x must be same. But if we find change in y over change x for this table. They won't be same. This table value can't be linear.

$\frac{142-118}{6-4}\neq \frac{150-142}{8-6}$

2) Quadratic: For quadratic equation. we will take standard form of quadratic equation $y=ax^2+bx+c$. Using any three value of table we will find a, b and c and then we satisfy other value of of table.

$y=ax^2+bx+c$

Point 1: (4,118) $\Rightarrow 118=16a+4b+c$

Point 2: (6,142) $\Rightarrow 142=36a+6b+c$

Point 3: (8,150) $\Rightarrow 150=64a+8b+c$

Now we have three equation and to solve for a, b and c. Using elimination method we get the value of a=-2, b=32 and c=22.

So, Quadratic equation $y=-2x^2+32x+22$

So, we get quadratic model for the given data in the table.

Answer 2

A quadratic function would fit this data.

The data does not increase at the same rate each time, so it is not linear.  It comes to a maximum at (8, 150) and decreases.  It decreases the same way it increased.  This would lead to a U-shaped graph, which indicates a quadratic function.