College Math Placement Practice Test

Given the function f(x) = x^2 - 4, what is the vertex of the parabola?

1. (0, 0)

2. (0, -4)

3. (-2, 0)

4. (-4, 0)

The correct answer is: (0, -4)

To find the vertex of the parabola described by the function \( f(x) = x^2 - 4 \), we can identify important characteristics of quadratic functions. This particular function is in the standard form \( f(x) = ax^2 + bx + c \), where \( a = 1 \), \( b = 0 \), and \( c = -4 \). The vertex of a parabola represented by a quadratic function can be found using the formula for the x-coordinate of the vertex: \[ x = -\frac{b}{2a} \] In this case, since \( b = 0 \): \[ x = -\frac{0}{2 \times 1} = 0 \] Next, to find the corresponding y-coordinate of the vertex, we substitute \( x = 0 \) back into the function: \[ f(0) = (0)^2 - 4 = -4 \] Thus, the vertex of the parabola is at the point \( (0, -4) \). This supports the conclusion that choice B, \( (0, -4) \), correctly represents the location of the vertex. Recognizing the features of