SOLUTION: The price of gasoline at a local station throughout the month of March is modeled by y=-0.014x^2+0.448x-2.324 where x=1 corresponds to March 1. a) On what day in March did the pri

Algebra ->  Rational-functions -> SOLUTION: The price of gasoline at a local station throughout the month of March is modeled by y=-0.014x^2+0.448x-2.324 where x=1 corresponds to March 1. a) On what day in March did the pri      Log On


   

Question 71253: The price of gasoline at a local station throughout the month of March is modeled by y=-0.014x^2+0.448x-2.324 where x=1 corresponds to March 1.
a) On what day in March did the price of gasoline reach it's maximum?
b) What was the highest price of gasoline in March?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The price of gasoline at a local station throughout the month of March is modeled by y=-0.014x^2+0.448x-2.324 where x=1 corresponds to March 1.
a) On what day in March did the price of gasoline reach it's maximum?
What you need to find is the vertex of the parabola represented by this function. The formula to find the vertex of a parabola represented by a quadratic function in the form of highlight%28y=ax%5E2%2Bbx%2Bc%29 is highlight%28x=-b%2F2a%29
a=-0.041 and b=0.448, so the price of gasoline reaches its maximum at:
x=-0.448%2F%282%28-0.014%29%29
x=16
Therefore the price reaches it's maximum on March 16.
b) What was the highest price of gasoline in March?
What you need to find is the y value of the vertex of the parabola. You can get this by plugging the x value of the parabola into the function for x and solve for y.
y=-0.014%2816%29%5E2%2B0.448%2816%29-2.324
y=1.26
You didn't mention how you were measuring the price of gasoline, it appears that the maximum price is $1.26 per gallon.
Happy Calculating!!!