all - star trinkets estimates its monthly profits using a quadratic function. the table shows the total…

all - star trinkets estimates its monthly profits using a quadratic function. the table shows the total profit as a function of the number of trinkets produced.\nall - star profits\n|trinkets produced x|monthly profit y|\n|----|----|\n|0| - 3125|\n|50|0|\n|100|1875|\n|150|2500|\n|200|1875|\n|250|0|\nwhich function can be used to model the monthly profit for x trinkets produced?\n○ f(x)=-4(x - 50)(x - 250)\n○ f(x)=-\frac{1}{4}(x - 50)(x - 250)\n○ f(x)=28(x + 50)(x + 250)\n○ f(x)=\frac{1}{28}(x + 50)(x + 250)

all - star trinkets estimates its monthly profits using a quadratic function. the table shows the total profit as a function of the number of trinkets produced.\nall - star profits\n|trinkets produced x|monthly profit y|\n|----|----|\n|0| - 3125|\n|50|0|\n|100|1875|\n|150|2500|\n|200|1875|\n|250|0|\nwhich function can be used to model the monthly profit for x trinkets produced?\n○ f(x)=-4(x - 50)(x - 250)\n○ f(x)=-\frac{1}{4}(x - 50)(x - 250)\n○ f(x)=28(x + 50)(x + 250)\n○ f(x)=\frac{1}{28}(x + 50)(x + 250)

Answer

Explanation:

Step1: Recall quadratic - function form

A quadratic function in factored form is (y = a(x - r_1)(x - r_2)), where (r_1) and (r_2) are the x - intercepts. From the table, the x - intercepts (where (y = 0)) are (x = 50) and (x = 250). So the function has the form (y=a(x - 50)(x - 250)).

Step2: Find the value of (a)

Substitute (x = 0) and (y=-3125) into (y=a(x - 50)(x - 250)). We get (-3125=a(0 - 50)(0 - 250)). First, simplify the right - hand side: ((0 - 50)(0 - 250)=(-50)\times(-250)=12500). Then, solve for (a): (a=\frac{-3125}{12500}=-\frac{1}{4}).

Answer:

(f(x)=-\frac{1}{4}(x - 50)(x - 250))