Answer:
See below.
Step-by-step explanation:
The graph of ƒ(x) = x² is the red parabola in Figure 1.
Step 1. Vertex of g(x)
g(x) = (x – 1)² + 2
The graph of g(x) will be a parabola like that of ƒ(x) translated one unit to the right and two units up.
The vertex of ƒ(x) is at (0, 0), so the vertex of g(x) is at (1, 2). See Figure 1.
Step 2. Calculate two more points
(a) Try x = 0
g(0) = (0 – 1)² + 2 = 1² + 2 = 1 + 2 = 3
So, there is a point at (0, 3).
(b) Try x = 2
The axis of symmetry is a vertical line passing through the vertex at x = 1. We have calculated a point one unit left of the axis (at x = 0), so let's calculate a point one unit to the right, at x = 2.
g(2) = (2 – 1)² + 2 = 1² + 2 = 1 + 2 = 3
So, there are points at (2, 3) and (1,3). See Figure 2.
Step 3. Sketch the graph of g(x)
Draw a smooth curve through the three points. Extend the arms of the parabola vertically so the graph has the same shape as that of ƒ(x).
Your graph should look like the blue parabola in Figure 3.
