C4L1 Notes
Quadratic Functions and Transformations
The anatomy of a parabola:
y
y-intercept:
axis of symmetry:
zero:
zero:
x
vertex:
minimum value:
domain (left to right):
range (lowest to highest):
Vertex form of the equation of a parabola: ܎ሺ‫ܠ‬ሻ =
Finding the vertex from vertex form: V:
Rigid transformations of quadratic functions:
Rigid transformations
* vertical shift c units up:
_______________
* vertical shift c units down:
_______________
* horizontal shift c units right:
_______________
* horizontal shift c units left:
_______________
* reflection on the x-axis:
_______________
* reflection on the y-axis:
_______________
Non-rigid transformations
_______________
* vertical stretch
_______________
* horizontal stretch
_______________
Identify the vertex and axis of symmetry of the equation of the parabola.
1. y =
2. f(x) =
Identify the minimum/maximum value of each.
3. y =
4. f(x) =
State the domain and range of the graph of the quadratic function.
5. y =
6. y =
State the intercepts of the graph of the quadratic equation.
7. y = (x – )2
8. y = x2 –
9. y = x2 +
11. y = - (x –
10. y = (x +
)2 +
)2 –
Sketch the graph of each quadratic function. State the steps that
transform the parent graph.
12. y = (x – )2
13. f(x) = x2 –
y
y
x
)2
14. f(x) = (x +
x
15. y = x2 +
y
y
x
x
16. y = (x –
)2 –
17. f(x) = – (x +
y
)2 +
y
x
૚
)2 +
18. y = 2 (x –
x
19. f(x) = (x +
૜
y
)2 –
y
x
x