the table shows some values that satisfy the quadratic equation. which of the following is a true statement…
the table shows some values that satisfy the quadratic equation. which of the following is a true statement? if the store charges $5 per soccer ball, it can expect to sell 170 of them. if the store charges $8 per soccer ball, it makes a daily profit of $236. if the store sells 12 soccer balls, it makes $156 in profit. the greater the selling price, the greater the profit. y = -6x^2 + 100x - 180 x = selling price of each soccer ball y = daily profit from soccer balls
Answer
Explanation:
Step1: Analyze option 1
The table gives profit when $x = 5$ is $y=170$, not the number of balls sold. So option 1 is false.
Step2: Analyze option 2
When $x = 8$, substitute into $y=-6x^{2}+100x - 180$. $y=-6\times8^{2}+100\times8 - 180=-6\times64 + 800-180=-384+800 - 180=236$. Option 2 is true.
Step3: Analyze option 3
The table gives profit based on selling - price $x$, not the number of balls sold. When $x = 12$, $y = 156$, not when 12 balls are sold. So option 3 is false.
Step4: Analyze option 4
The function $y=-6x^{2}+100x - 180$ is a quadratic function with $a=-6<0$, so it is a parabola opening down - ward. There is a maximum point, and the profit does not increase with the increase of the selling price all the time. So option 4 is false.
Answer:
If the store charges $8 per soccer ball, it makes a daily profit of $236.