Example 1

Given the following quadratic functions in vertex form, determine the vertex of each corresponding parabola.

1. \(f(x) = 1.5(x - 2)^2 + 6\)
   
   
   Solution

   The vertex of \(f(x) = a(x - p)^2 + q \) is \((p, q) \). In this case, \(p = 2\) and \(q = 6\). The vertex is \((2, 6)\).
2. \(g(x) = -(x - 2)^2 - 10\)
   
   
   Solution

   For this example, \(p = 2\) and \(q = −10\). The vertex is \((2, −10)\).
3. \(h(x) = 5(x + 3)^2 + 8\)
   
   
   Solution

   For this example, \(p = −3\) and \(q = 8\). The vertex is \((−3, 8)\).