The company discovered that it costs $30 to produce 2 widgets, $118 to produce 4 widgets, and $766 to produce 10. Find the cost of producing 6 widgets. Use the quadratic function to solve

Question

The company discovered that it costs $30  to produce 2 widgets, $118 to produce 4 widgets, and $766 to produce 10. Find the cost of producing 6 widgets. Use the quadratic function to solve

anonymous · Answer

You're told the function you should be looking for is quadratic, and you have three (x,y) points to use.

The general form of the quadratic is$$y=ax^2+bx+c$$If you substitute each pair of points, you'll end up with three linear equations in the constants, a, b and c.  You can then solve these using linear algebra.
So, for the first point, (2,30),$$30 = a(2^2)+b(2)+c \rightarrow 30=4a+2b+c$$That's equation 1.

anonymous · Answer

For (4,118),$$118=16a+4b+c$$and for (10,766),$$766=100a^2+10b+c$$

anonymous · Answer

sorry, typo on last one. Should be$$766=100a+10b+c$$

anonymous · Answer

Can you take it from here?  You use these three equations to solve for a, b and c.  Then you can set up your quadratic, and plug in x=6 to get the cost.

anonymous · Answer

probably not. seeing i'm completely confused and my online courses don't really do enough explaining for math.