Question: Choose the graph that represents the function. $f(x) = (x - 2)^2 - 4$ Choose the correct graph…

Choose the graph that represents the function.

$f(x) = (x - 2)^2 - 4$

Choose the correct graph from the choices on the right.

A. B. C. D.

Solution

The problem is asking you to choose the graph that represents the function: \[ f(x) = (x - 2)^2 - 4 \] This function is a quadratic equation in vertex form, where the vertex is at \((h, k)\). Here, \(h = 2\) and \(k = -4\), so the vertex of the parabola is at \((2, -4)\). The graph should be a parabola opening upwards, with its lowest point at \((2, -4)\). To find the correct graph: 1. Locate the vertex of the function \((2, -4)\) on the graph. 2. Ensure the parabola opens upwards from this vertex. The correct graph will have these characteristics. Check the options provided and select the one that matches this description.