Analyzing the Function f(x) = (x – 3)2 and Determining the Corresponding Graph

Which graph represents the function f(x) = (x – 3)2?

To determine which graph represents the function f(x) = (x – 3)2, let’s analyze the given function and understand its characteristics

To determine which graph represents the function f(x) = (x – 3)2, let’s analyze the given function and understand its characteristics.

The function f(x) = (x – 3)2 is in vertex form, where the vertex point is (3, 0). This means that the graph of this function is a parabola that opens upwards or downwards, depending on the coefficient before the squared term.

In vertex form, the general equation is y = a(x – h)2 + k, where (h, k) represents the vertex point.

Given that the vertex point is (3, 0), we can substitute these values into the equation:

y = a(x – 3)2 + 0
y = a(x – 3)2

Since k = 0, the coefficient of the squared term does not affect the vertex point and only determines the direction of the parabola (upward or downward).

To determine the direction, consider the sign of the coefficient “a”. If “a” is positive, the parabola opens upwards, and if “a” is negative, the parabola opens downwards.

In this case, since “a” is not specified, we assume it to be positive. Therefore, the parabola opens upwards.

Now, let’s analyze the graphs and determine which one represents the function f(x) = (x – 3)2.

Graph 1:
The graph shows a parabola that opens upwards and passes through the point (3, 0).

Graph 2:
The graph shows a parabola that opens downwards and passes through the point (3, 0).

Graph 3:
The graph shows a straight line passing through the point (3, 0).

Since the given function f(x) = (x – 3)2 represents a parabola that opens upwards and passes through the point (3, 0), the only graph that corresponds to this function is Graph 1.

Therefore, Graph 1 represents the function f(x) = (x – 3)2.

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