Answer:
(1), (3)
Step-by-step explanation:
5. If m starts at 1, a geometric series has the form a₁ (r)ᵐ⁻¹.
If m starts at 0, a geometric series has the form a₀ (r)ᵐ.
Here, m starts at 0. The first term, a₀, is 150. The temperature is decreasing, so we're looking for an r < 1. Therefore, the answer must be (1) 150 (0.85)ᵐ.
7. A quadratic written in vertex form is:
y = a(x - h)² + k
We can find the vertex of the parabola using x = -b/(2a).
x = -12 / (2*3)
x = -2
f(-2) = 3(-2)² + 12(-2) + 11
f(-2) = -1
So the vertex (h, k) is at (-2, -1).
Therefore, the answer must be f(x) = 3(x + 2)² - 1
We can also show this by completing the square.
f(x) = 3x² + 12x + 11
f(x) = 3(x² + 4x) + 11
f(x) = 3(x² + 4x + 4) - 3(4) + 11
f(x) = 3(x + 2)² - 1
