Question

which of the following shows the graph of (y = 3(x - 2)^2 - 2)?

Explanation:

Step1: Identify the vertex

The vertex form is \(y = a(x-h)^2 + k\), giving vertex \((2, -2)\).

$$(h, k) = (2, -2)$$

Step2: Determine the direction

Since \(a = 3 > 0\), the parabola opens upward.

$$a = 3 > 0$$

Step3: Find the y-intercept

Substitute \(x = 0\) to find the y-intercept.

$$y = 3(0-2)^2 - 2 = 10$$

Step4: Match with the correct graph

The top-right graph has its vertex at \((2, -2)\) and opens upward.

$$\text{Vertex} = (2, -2)$$

Answer:

The top-right graph.