Answer: The price of maximum sales is $160
Step-by-step explanation:
This question requires you to find the vertex of this equation. The vertex of a parabola is the point where the parabola crosses its axis of symmetry.
since the coefficient of the [tex]x^2[/tex] term is negative, the vertex will be the highest point on the graph.
this quadratic equation is in standard form: [tex]y = ax^2+bx+c[/tex].
From this, we can derive:
[tex]a = -3[/tex]
[tex]b = 60[/tex]
[tex]c = 1060[/tex]
First, determine the axis of symmetry ([tex]p[/tex] is the variable for the horizontal axis ([tex]x[/tex]) in this instance). This will be our x-coordinate of the vertex.
[tex]p = \frac{-b}{2a}[/tex]
[tex]p = \frac{-(60)}{2(-3)}[/tex]
[tex]p = \frac{-60}{-6}[/tex]
[tex]p=10[/tex]
Then, substitute the axis of symmetry into the function to find the y coordinate of the axis of symmetry. r stands for the variable for the vertical axis in this instance. This will be our y-coordinate of the vertex.
[tex]r = -3(10)^2+60(10)+1060[/tex]
[tex]r = 160[/tex]
As we have determined both the x and y coordinate of the vertex for this equation, we can determine that the maximum point is at [tex](10, 160)[/tex].
the maximum price ([tex]r[/tex]) is 160