# FNGR 2 | Lesson 4 | Making Connections Solutions

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).