Question

When graphing f (x) = 2(x – 4)2 – 1, what is the next point you should graph counting from the vertex?

A) (3, -1)
B) (4, -1)
C) (5, -1)
D) (6, -1)

Answer 1

The next point to graph for the parabola f(x) = 2(x - 4)² - 1, after the vertex, is at (5, 1), which is not listed in the provided options. Therefore, there seems to be an error in the options given since the correct point is not included.

Step-by-step explanation:

When graphing f(x) = 2(x – 4)2 – 1, the next point you should graph counting from the vertex can be determined by understanding that this equation represents a parabola. The vertex of this parabola is at the point (4, -1), where x=4 is the axis of symmetry for the parabola. To find the next point, we simply move one unit to the left or right of the vertex along the x-axis and calculate the corresponding y-value. Moving one unit to the right brings us to x=5. Substituting x=5 into the original equation, we get f(5) = 2(5 - 4)2 – 1 = 2(1)2 – 1 = 2 – 1 = 1. So the next point is (5, 1), making (C) the correct answer.