Question

Arrange the parabolas with respect to the position of their vertices from left to right.

a. y = f(x-7)

b. y = f(1-4)

c. y = f(x+2)

d. y = f(1-1)

Answer 1

To arrange the parabolas by the positions of their vertices from left to right, we must understand the transformations applied to f(x). Parabolas with terms (x + 2), (x - 1), (x - 4), and (x - 7), have their vertices moving left or right depending on the positive or negative sign in front of the numbers. The correct order from left to right, considering likely typos, is y = f(x + 2), y = f(x - 1), y = f(x - 4), and y = f(x - 7).

Step-by-step explanation:

To arrange the parabolas with respect to the position of their vertices from left to right, we need to consider the transformations applied to the function f(x). The general form of a parabola is y = f(x), and when we apply a transformation inside the function, it affects the horizontal position of the vertex.

• y = f(x - 7) has its vertex moved 7 units to the right.
• y = f(1 - 4) appears to be a typo, but if it meant y = f(x - 4), then the vertex would be 4 units to the right.
• y = f(x + 2) has its vertex moved 2 units to the left.
• y = f(1 - 1) seems to be another typo, and if it meant y = f(x - 1), then the vertex would be 1 unit to the right.

Assuming that '1 - 4' and '1 - 1' are typographical errors, and they should be x - 4 and x - 1 respectively, arranging the parabolas from left to right by the position of their vertices is:

1. y = f(x + 2)
2. y = f(x - 1)
3. y = f(x - 4) or y = f(1 - 4) if it's not a typo
4. y = f(x - 7)