1. 2.1 – Quadratic Functions

2. In this section, you will learn to
analyze graphs of quadratic functions
write quadratic functions in standard form and sketch its graphs
solve real-life problems

3. Definition of a Polynomial Function:

4. Definition of a Quadratic Function:
a) Axis of symmetry:
the line where the
parabola is symmetric
b) Vertex: The point
where the axis of
symmetry intersects
the parabola

5. Definition of a Quadratic Function:
c) Upward or Downward:
If the leading coefficient is
positive (a>0) , the parabola
opens upward.

6. Definition of a Quadratic Function:
c) Upward or Downward:
If the leading coefficient is
negative (a<0) , the parabola
opens downward.

7. Definition of a Quadratic Function:
d) Minimum or Maximum: If the parabola opens upward, the vertex has a minimum value. If the parabola opens downward, the vertex has a maximum value.

8. Standard Form of a Quadratic Function:
a) Vertex:
b) Axis of Symmetry:
c) Vertex:
Therefore,
* To write an equation in standard
form, you need to complete the square.

9. Identify the vertex and axis of symmetry for
There are two methods to identify the vertex and the axis of symmetry.
Method 1:

10. Method 2: Complete the Square

11. Complete the Square:

12. Method 2: Complete the Square

13. Identify the vertex and zeros to graph:

14. Identify the vertex and zeros to graph:
Vertex: Zeros:

15. Find the quadratic equation in standard form:

16. Find the quadratic equation in standard form:
Vertex:
Point:

17. Real-Life Example:

18. Real-Life Example:
Since this parabolic path is opening
downward, the maximum height is reached at
the vertex point. You can use the formulas
for h and k to find the vertex point. Then,
the maximum height is represented by the k
value.

19. Real-Life Example:
The maximum height reached by this ball
is 130 ft.

20. Graph:
The maximum height reached by this ball is
130 ft.

21. Real-Life Example:

22. Real-Life Example:
Since this parabolic path is opening upward,
the minimum height is reached at the vertex
point. You can use the formulas for h and k
to find the vertex point. Then, the minimum
height is represented by the k value.

23. Real-Life Example:
The minimum height reached by the yo-yo is
16 feet.

24. Real-Life Example:
The minimum height reached by the yo-yo is
16 feet.