SOLUTION: This is actually a word problem, but it needs to be graphed to find the parabola along with the solution and I don't know where to begin: A company uses the formula C(x) = 0.02x

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Question 57392: This is actually a word problem, but it needs to be graphed to find the parabola along with the solution and I don't know where to begin:
A company uses the formula C(x) = 0.02x^2 - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?
Can someone PLEASE help?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
A company uses the formula C(x) = 0.02x^2 - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?
:
The x value of the vertex is the number of bars for which the unit cost is at its minimum.
We can find that by:
When a quadratic equation is in standard form: highlight%28ax%5E2%2Bbx%2Bc%29
In what you typed, a=0.02 b=-3.4, and c=150
The x value of the vertex is found by this formula:highlight%28x=-b%2F2a%29
x=-%28-3.4%29%2F%282%28.02%29%29
highlight%28x=85%29
85 is the number of bars at which the unit cost is at its minimum.
:
The unit cost at that level would be: C(-b/2a)
Just substitute the x-value of the vertex into the C(x) function and solve.
C%2885%29=0.02%2885%29%5E2-3.4%2885%29%2B150
C%2885%29=0.02%287225%29-3.4%2885%29%2B150
C%2885%29=144.5-289%2B150
C%2885%29=5.5
The unit cost at that level is: C=$5.50
Check that against what you got.
Happy Calculating!!!