SOLUTION: The National Gizmo Corporation calculates that its profit, in thousands of dollars, on the sale of x thousand gismos is given by p(x)= -2x^2 + 52x + 30. How many gizmos must be sol

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The National Gizmo Corporation calculates that its profit, in thousands of dollars, on the sale of x thousand gismos is given by p(x)= -2x^2 + 52x + 30. How many gizmos must be sol      Log On


   

Question 183985: The National Gizmo Corporation calculates that its profit, in thousands of dollars, on the sale of x thousand gismos is given by p(x)= -2x^2 + 52x + 30. How many gizmos must be sold in order to earn a maximum profit?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
p(x)= -2x^2 + 52x + 30
.
By inspection, looking at the leading coefficient 'a' (-2) we see that since it is NEGATIVE, it is a parabola that opens downward (negative/sad face).
.
That being said, the "axis of symmetry" should provide your answer. To find it:
-b/2a
= -52/2(-2)
= -52/-4
= 13 thousands