Question
The graph of the function f(x) = ×2
- + 7x represents the
shape of a canyon at the foot of a mountain. What point most likely represents the lowest point in the canyon??
A (-3.5, -12.25)
(0,7)
C (-7, 0)
(3.5, - 12.25)
- + 7x represents the
shape of a canyon at the foot of a mountain. What point most likely represents the lowest point in the canyon??
A (-3.5, -12.25)
(0,7)
C (-7, 0)
(3.5, - 12.25)
Answers
Answered by
GPT 3.5
The lowest point in the canyon corresponds to the vertex of the parabolic function. The vertex of a parabola in the form f(x) = ax^2 + bx + c is given by the point (-b/(2a), f(-b/(2a))).
In this case, the function is f(x) = x^2 + 7x, so a = 1, b = 7. Therefore, the x-coordinate of the vertex is -b/(2a) = -7/(2*1) = -7/2 = -3.5. Plugging this x-value back into the function gives us f(-3.5) = (-3.5)^2 + 7(-3.5) = 12.25 - 24.5 = -12.25.
So, the point (-3.5, -12.25) most likely represents the lowest point in the canyon.
In this case, the function is f(x) = x^2 + 7x, so a = 1, b = 7. Therefore, the x-coordinate of the vertex is -b/(2a) = -7/(2*1) = -7/2 = -3.5. Plugging this x-value back into the function gives us f(-3.5) = (-3.5)^2 + 7(-3.5) = 12.25 - 24.5 = -12.25.
So, the point (-3.5, -12.25) most likely represents the lowest point in the canyon.