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put this solution on YOUR website!"A model of the daily profits "p"of a gas station based on the price per gallon "g" is: p=-15000g^2 + 34500g-16800. Use the discriminant to find if the station can profit $4000 per day. Explain"
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p=-15000g^2 + 34500g-16800
Disc = b^2 - 4ac = 34500^2 - 4*15000*16800
Disc = 182250000
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The discriminant is +, meaning there are 2 values of g that give p=0, or break even.
The Disc doesn't directly answer the question.
"Use the discriminant" makes no sense.
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Find the max of the function.
It's a parabola, so the max is at the vertex
The vertex is on the LOS, the Line of Symmetry, or Axis of Symmetry
The eqn of the LOS is g = -b/2a = -34500/2*-15000
LOS is g = 1.15
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Find p at g = 1.15
p = -15000*1.15^2 + 34500*1.15 - 16800
p = $3037.50
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That's the max profit per day using that function.
