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 \((h, k)\).
Return to Making Connections (Quadratics and Horizontal Shifts)