Part A
a. This is the parent function, vertex at (0,0)
b. The function is shifted to the left 2, vertex at (-2, 0)
c. The function is shifted to the right 3, vertex at (3,0)
d. The function is shifted to the right 5, vertex at (5,0)
\(f(x) = (x – h)^2\), the function is shifted to the right \(h\)
\(f(x) = (x + h)^2\), the function is shifted to the left \(h\)
Part B
For example: \(f(x) = (x + 3)^2 + 2\), the graph is shifted to the left 3 and up 2. So the vertex is at \((-3, 2)\). When \(f(x) = (x – 1)^2 -4\), the graph is shifted to the right 1 and down 4. Therefore in general, in the function, \(f(x) = (x – h)^2 + k\) the vertex is at (h, k).