Final answer:
The coordinates of the vertex are (1, 6) and the equation of the axis of symmetry is x = 1. Option A is correct.
Step-by-step explanation:
To find the coordinates of the vertex of the function, we need to find the value of t that corresponds to the maximum or minimum point of the parabola. The vertex is given by the values (t, f(t)), where t is the x-coordinate.
The axis of symmetry is a vertical line that passes through the vertex. It has the equation x = t.
Given the function f(t) = -1.5t + 3t + 2, we can determine the vertex and axis of symmetry as follows:
Step 1: Identify the coefficient of the quadratic term, a. In this case, a = -1.5.
Step 2: Use the formula t = -b / (2a) to find the x-coordinate of the vertex. The coefficient of the linear term, b, is 3.
t = -3 / (2*(-1.5)) = 3 / 3 = 1.
Therefore, the vertex is (1, f(1)).
Step 3: Substitute the value of t into the function to find the y-coordinate of the vertex.
f(1) = -1.5(1) + 3(1) + 2 = 1 + 3 + 2 = 6.
Therefore, the vertex is (1, 6).
Hence, the correct answer is A) Vertex: (1, 6), Axis of Symmetry: x = 1. Option A is correct.
Complete question:
What are the coordinates of the vertex and the equation of the axis of symmetry for the function:
f(x) = - 1.5t + 3t + 2"
A) Vertex: (1, 6), Axis of Symmetry: x = 1
B) Vertex: (2, 3), Axis of Symmetry: x = 2
C) Vertex: (1.5, 1), Axis of Symmetry: x = 1.5
D) Vertex: (3, 2), Axis of Symmetry: x = 2