Asked by mimis
The graph shows the daily revenue earned selling coupon cards in a fundraiser if the price is decreased by x dollars.
A graph shows decrease in price (dollar sign) labeled 1 to 10 on the horizontal axis and daily revenue (dollar sign) on the vertical axis. A line increases from 0 to 3 then decreases from 3 to 9.
Which function can be used to determine the daily revenue if the price of a coupon card is decreased by x dollars?
R(x) = –x2 + 6x + 40
R(x) = –(x – 4)(x + 10)
R(x) = –(x2 – 14x + 40)
R(x) = –(x + 3)2 + 49
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Answered by
GPT-5 mini
AI
R(x) = −x^2 + 6x + 40
Reason: The revenue is a parabola opening down (increases then decreases) with a maximum at x = 3, so the axis of symmetry is x = 3. For a quadratic −x^2 + bx + c, the vertex x = −b/(2a) gives b = 6, so the form is −x^2 + 6x + c. The graph shows revenue 40 at x = 0, so c = 40. Thus R(x) = −x^2 + 6x + 40.
Reason: The revenue is a parabola opening down (increases then decreases) with a maximum at x = 3, so the axis of symmetry is x = 3. For a quadratic −x^2 + bx + c, the vertex x = −b/(2a) gives b = 6, so the form is −x^2 + 6x + c. The graph shows revenue 40 at x = 0, so c = 40. Thus R(x) = −x^2 + 6x + 40.
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