Both functions are quadratic but differ in their constant terms, nature of solutions, vertex positions, and overall shapes of their graphs.
**Comparison:**
1. Both \(f(x) = x^2 - 4\) and \(g(x) = x^2 + 4\) are quadratic functions.
2. They both have the same quadratic term, \(x^2\).
**Contrast:**
1. **Constant Term:** \(f(x)\) has a constant term of \(-4\), while \(g(x)\) has a constant term of \(4\).
2. **Nature of Solutions:** \(f(x)\) has real roots when \(x = 2\) or \(x = -2\), making it factorable into \((x - 2)(x + 2)\). \(g(x)\) has no real roots, as its constant term is positive, resulting in complex roots.
3. **Vertex:** The vertex of \(f(x)\) is a minimum point at \((0, -4)\), while the vertex of \(g(x)\) is a minimum point at \((0, 4)\).
4. **Graphs:** \(f(x)\) opens upwards, forming a parabola that opens upwards, while \(g(x)\) opens upwards as well but is shifted upwards due to the positive constant term.
In summary, both functions are quadratic but differ in their constant terms, nature of solutions, vertex positions, and overall shapes of their graphs.