1. 4.1 Quadratic Functions and Transformations
Learning Goal
identify and graph quadratic functions

2. Vocabulary
parabola : the graph of a quadratic function vertex : minimum or maximum value; where the parabola intersects the axis of symmetry axis of symmetry : a line that divides the parabola into 2 parts, mirror images

3. Finding the vertex of a parabola
equation
vertex
vertex form

4. Translating a parabola
vertex form : the graph of translated h units horizontally and k units vertically h k
positive
right up
negative
left
down
vertex: axis of symmetry:

5. Ex 1
Graph each function. How is each graph a translation of ?

6. Reflecting a parabola
vertex form : the graph of reflected in the x-axis
value of a
direction of opening
min/max value
range
graph
positive up
minimum
negative
down
maximum

7. Ex 2
Determine the direction of opening for each quadratic function. Determine if the function has a minimum or maximum and state its value.

8. Stretching or compressing a parabola
compression
0 < a < 1

9. Ex 3
Determine if each quadratic function is stretched or compressed.

10. Ex 3
Graph. Find the vertex, axis of symmetry, y-intercept, maximum or minimum, the domain and range.
vertex
aos
y-intercept SP
max/min
domain
range

11. Ex 4
Graph. Find the vertex, axis of symmetry, y-intercept, maximum or minimum, the domain and range.
vertex
aos
y-intercept SP
max/min
domain
range

12. Writing the equation of a parabola
Ex 4
Write an equation of the quadratic function in vertex form with

13. EX 5 Write the equation in vertex form of the given parabola.
Convert your answer to standard form.

14. Ex 6
Write a quadratic function in vertex form that models the path of the dolphin’s jump.