Question

graph the function.
$k(x) = (x - 1)^2$

Explanation:

Step1: Identify the vertex form

The function \( k(x) = (x - 1)^2 \) is in vertex form \( y = a(x - h)^2 + k \), where \( a = 1 \), \( h = 1 \), and \( k = 0 \). So the vertex is at \( (1, 0) \).

Step2: Find additional points

• When \( x = 0 \), \( k(0) = (0 - 1)^2 = 1 \), so the point is \( (0, 1) \).
• When \( x = 2 \), \( k(2) = (2 - 1)^2 = 1 \), so the point is \( (2, 1) \).
• When \( x = 3 \), \( k(3) = (3 - 1)^2 = 4 \), so the point is \( (3, 4) \).
• When \( x = -1 \), \( k(-1) = (-1 - 1)^2 = 4 \), so the point is \( (-1, 4) \).

Step3: Plot the vertex and points

Plot the vertex \( (1, 0) \), and the points \( (0, 1) \), \( (2, 1) \), \( (3, 4) \), \( (-1, 4) \). Then draw a parabola (since \( a = 1 > 0 \), it opens upwards) through these points.

Answer:

The graph is a parabola opening upwards with vertex at \((1, 0)\), passing through points like \((0, 1)\), \((2, 1)\), \((3, 4)\), \((-1, 4)\) (plotted on the given coordinate grid).