the quadratic function y = -10x² + 160x - 430 models a stores daily profit (y), in dollars, for selling t…

the quadratic function y = -10x² + 160x - 430 models a stores daily profit (y), in dollars, for selling t - shirts priced at x dollars.\na the daily profit the company would make from the t - shirts if it gave the t - shirts away for free\nb the greatest daily profit the company could make from selling the t - shirts\nc a selling price that would result in the company making no profit from the t - shirts\nd the selling price that would result in the company making the greatest daily profit from the t - shirts\nmatch each item with what it represents in this situation by entering the appropriate letter in each box.\nx - coordinate of the vertex of the function\ny - coordinate of the vertex of the function\nan x - intercept of the function\na y - intercept of the function\ndone

the quadratic function y = -10x² + 160x - 430 models a stores daily profit (y), in dollars, for selling t - shirts priced at x dollars.\na the daily profit the company would make from the t - shirts if it gave the t - shirts away for free\nb the greatest daily profit the company could make from selling the t - shirts\nc a selling price that would result in the company making no profit from the t - shirts\nd the selling price that would result in the company making the greatest daily profit from the t - shirts\nmatch each item with what it represents in this situation by entering the appropriate letter in each box.\nx - coordinate of the vertex of the function\ny - coordinate of the vertex of the function\nan x - intercept of the function\na y - intercept of the function\ndone

Answer

Explanation:

Step1: Analyze y - intercept

The y - intercept is found by setting (x = 0). When (x=0), (y=- 10(0)^2+160(0)-430=-430). This represents the daily profit when the T - shirts are given away for free ((x = 0)). So the y - intercept corresponds to A.

Step2: Analyze vertex x - coordinate

For a quadratic function (y = ax^{2}+bx + c), the x - coordinate of the vertex is given by (x=-\frac{b}{2a}). For (y=-10x^{2}+160x - 430), (a=-10) and (b = 160), so (x=-\frac{160}{2\times(-10)} = 8). This is the selling price that results in the greatest daily profit, so the x - coordinate of the vertex corresponds to D.

Step3: Analyze vertex y - coordinate

Substitute the x - coordinate of the vertex ((x = 8)) into the function (y=-10(8)^{2}+160(8)-430=-10\times64 + 1280-430=-640+1280 - 430 = 210). This is the greatest daily profit, so the y - coordinate of the vertex corresponds to B.

Step4: Analyze x - intercept

The x - intercepts are found by setting (y = 0), i.e., (-10x^{2}+160x - 430 = 0). Solving this equation gives the selling prices that result in no profit. So the x - intercept corresponds to C.

Answer:

x - coordinate of the vertex of the function: D y - coordinate of the vertex of the function: B an x - intercept of the function: C a y - intercept of the function: A