Question

graph the parabola

( y = (x - 1)^2 + 2 )

plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph-a-function button.

Explanation:

Step1: Find the vertex

The equation of the parabola is in vertex form \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For \( y=(x - 1)^2+2 \), \( h = 1 \) and \( k = 2 \), so the vertex is \((1, 2)\).

Step2: Find points to the left of the vertex

Choose \( x = 0 \) (left of \( x = 1 \)): Substitute into the equation: \( y=(0 - 1)^2+2=1 + 2 = 3 \), so the point is \((0, 3)\).
Choose \( x=-1 \) (left of \( x = 1 \)): Substitute: \( y=(-1 - 1)^2+2=4 + 2 = 6 \), so the point is \((-1, 6)\).

Step3: Find points to the right of the vertex

Choose \( x = 2 \) (right of \( x = 1 \)): Substitute: \( y=(2 - 1)^2+2=1 + 2 = 3 \), so the point is \((2, 3)\).
Choose \( x = 3 \) (right of \( x = 1 \)): Substitute: \( y=(3 - 1)^2+2=4 + 2 = 6 \), so the point is \((3, 6)\).

Answer:

Vertex: \((1, 2)\), Left points: \((0, 3)\), \((-1, 6)\), Right points: \((2, 3)\), \((3, 6)\) (These points can be plotted on the graph to sketch the parabola)