For a certain frozen pizza, as the cost goes from $2 to $4, the demand can be modeled by the formula y = -10x2 + 60x + 180, where x represents the cost and y represents the number of pizzas sold. Estimate the cost that will result in the greatest demand.

Answer: The cost that will result in the greatest demand is $3Step-by-step explanation:Letx ------> represents the cost  y -----> represents the number of pizzas soldwe have[tex]y=-10x^{2}+60x+180[/tex]This is a quadratic equation (vertical parabola) open downwardThe vertex is a maximumTo find out the greatest demand calculate the vertexThe equation of a vertical parabola in vertex form is equal to[tex]y=a(x-h)^{2}+k[/tex]where(h,k) is the vertexConvert the quadratic equation in vertex formComplete the squares[tex]y-180=-10x^{2}+60x[/tex]Factor the leading coefficient[tex]y-180=-10(x^{2}-6x)[/tex][tex]y-180-90=-10(x^{2}-6x+9)[/tex][tex]y-270=-10(x^{2}-6x+9)[/tex]Rewrite as perfect square[tex]y-270=-10(x-3)^{2}[/tex][tex]y=-10(x-3)^{2}+270[/tex] ----> equation in vertex formThe vertex is the point (3,270)thereforeFor the greatest demandThe cost is $3The number of pizzas sold is 270