Answer: 9637
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Step-by-step explanation:
You can use your calculator to make short work of this problem. Simply plot the parabola and use the "minimum" feature on the calculator to spot the lowest point (specifically the coordinates of that point).
However, I have a feeling your teacher wants you to use a bit of math here. So I'll focus on another approach instead.
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The parabolic equation is of the form y = ax^2+bx+c
In this case, we have
Use the values of 'a' and b to find the x coordinate of the vertex h
h = -b/(2a)
h = -(-192)/(2*0.3)
h = 320
The x coordinate of the vertex is 320.
Plug this into the original equation to find the y coordinate of the vertex.
y = 0.3x^2 - 192x + 40357
y = 0.3(320)^2 - 192(320) + 40357
y = 9637 which is the minimum unit cost, in dollars.
The vertex is (h,k) = (320, 9637). It is the lowest point on this parabola.
Interpretation: If the company made 320 cars, then the unit cost (aka cost per car) is the smallest at $9637 per car.