1. Warm up
Using the distance formula, d = , to find the distance between the following sets of points:
1) (2, 5) and (-4, 7) 2) (-1, 0) and (-8, 4)

3. Transformations of quadratic functions
2.1 Notes:
Transformations of quadratic functions

4. Vertex form of quadratic functions
Quadratic functions, whose parent function is f(x) = x2, can be written in several forms. The form we are most familiar with is vertex form;
Vertex form: f(x) = a(x – h)2 + k
“a” is the stretch or shrink
“h” is the x –value of the vertex (opposite sign of what is given)
“k” is the y – value of the vertex
The vertex then is at (h, k) and that is the translation of the function.

5. Let’s try a few: 1) g(x) = (x + 4)2 – 1 2) h(x) = (x – 3) 2
3) r(x) = (x – 2)2 – 2
4) b(x) = (x + 5)2 + 1

6. Reflections, stretches and shrinks:
Reflection over the x – axis: f(x) = -x2
A reflection “flips” the graph upside down.
VERTICAL stretch: a > 1 outside the parenthesis, f(x) = 3x2
VERTICAL shrink: 0 < a < 1 outside the parenthesis, f(x) = x2
Vertical stretches and shrinks basically multiply the y values on our t-table by the “a” value.

7. Let’s try a few: 1) h(x) = - x2 2) g(x) = 3x2 3) f(x) = - x2 – 2
4) d(x) = -(x + 3)2 + 2

8. Writing equations of transformations
Follow the outline:
f(x) = reflection (x +/- left/right)2 +/- up/down
1) the graph of “g” is vertically stretched by a factor of 2, reflected over the x-axis and translated down 3 units.
2) the graph of “h” is reflected over the x-axis then translated up 4 units and left 2 units.
3) the graph of “c” has a vertex at (3, -7) and is vertically shrunk by a factor of

9. HW: p. 52 – 53 #9 – 39 odd