Final answer:
To find the vertical distance v between the line y = x - 6 and the parabola y = x² for -2 ≤ x ≤ 3, subtract the y-values of the line from the y-values of the parabola at each x-value within the given range. The function that gives the vertical distance is v = 12.
Step-by-step explanation:
To find the vertical distance v between the line y = x - 6 and the parabola y = x² for -2 ≤ x ≤ 3, we need to find the difference in the y-values of the two equations.
First, find the y-value of the line at x = -2 and x = 3. For x = -2, the y-value of the line is (-2) - 6 = -8. For x = 3, the y-value of the line is (3) - 6 = -3.
Next, find the y-value of the parabola at x = -2 and x = 3. For x = -2, the y-value of the parabola is (-2)² = 4. For x = 3, the y-value of the parabola is (3)² = 9.
Finally, subtract the y-values of the line from the y-values of the parabola to find the vertical distance v. For x = -2, v = 4 - (-8) = 12. For x = 3, v = 9 - (-3) = 12.
So, the function that gives the vertical distance v between the line y = x - 6 and the parabola y = x² for -2 ≤ x ≤ 3 is v = 12.