1. Graphing Quadratic Functions in Vertex form
Section
5.1
Graphing Quadratic Functions in Vertex form

2. Graphing Quadratic Functions
When quadratics are graphed they look like a U or an upside down U
if a > 0,
If a < 0,
The highest point or lowest point on the parabola is the _________.
_____________is the line that runs through the vertex and through the middle of the parabola.

3. Parabolas Basic (parent function) of a parabola y = x2
Vertex will be at
next two points will be at and

4. Example Graph f(x) = x2. Note that a = 1 in standard form.
Which way does it open?
What is the vertex?
What is the axis of symmetry?

5. Graph Quadratic Functions of the Form f(x) = x2 + k.
Objective 1
Graph Quadratic Functions of the Form f(x) = x2 + k.

6. Graphing Quadratic Functions
Graphing the Parabola Defined by f(x) = x2 + k
If k is positive, the graph of f(x) = x2 + k is the graph of y = x2 shifted
If k is negative, the graph of f(x) = x2 + k is the graph of y = x2 shifted

7. Example Graph f(x) = x2. Note that a = 1 in standard form.
Which way does it open?
What is the vertex?
What is the axis of symmetry?
Graph g(x) = x2 + 3 and h(x) = x2 – 3.
What is the vertex of each function?
What is the axis of symmetry of each function?

8. Example (cont) x y
f(x) = x2
g(x) = x2 + 3
h(x) = x2 – 3

9. Graph Quadratic Functions of the Form f(x) = (x – h)2 .
Objective 2
Graph Quadratic Functions of the Form f(x) = (x – h)2 .

10. Graphing the Parabola Defined by f(x) = (x – h)2
If h is positive, the graph of f(x) = (x – h)2 is the graph of y = x2 shifted to the
If h is negative, the graph of f(x) = (x – h)2 is the graph of y = x2 shifted to the

11. Example
Graph f(x) = x2. Graph g(x) = (x – 3)2 and h(x) = (x + 3)2. What is the vertex of each function? What is the axis of symmetry of each function?
Continued

12. Example (cont)
f(x) = x2
g(x) = (x – 3)2
h(x) = (x + 3)2

13. Graph Quadratic Functions of the Form f(x) = (x – h)2 + k.
Objective 3
Graph Quadratic Functions of the Form
f(x) = (x – h)2 + k.

14. Graphing the Parabola Defined by f(x) = (x – h)2 + k
The parabola has the same shape as y = x2.
The vertex is (h, k), and the axis of symmetry is the vertical line x = h.

15. Example
Graph g(x) = (x – 2)2 + 4.
Continued

16. Example (cont)
f(x) = x2
g(x) = (x – 2)2 + 4

17. Graph Quadratic Functions of the Form f(x) = ax2 .
Objective 4
Graph Quadratic Functions of the Form f(x) = ax2 .

18. Graphing the Parabola Defined by f(x) = ax2
If a is positive,
if a is negative,.
If |a| > 1, the graph of the parabola is than the graph of y = x2.
If |a| < 1, the graph of the parabola is than the graph of y = x2.

19. Example Graph f(x) = x2. Graph g(x) = 3x2 and h(x) = (1/3)x2.
How do the shapes of the graphs compare?
Continued

20. Example (cont) x y
f(x) = x2
g(x) = 3x2
h(x) = (1/3)x2

21. Graph Quadratic Functions of the Form f(x) = a(x – h)2 + k.
Objective 5
Graph Quadratic Functions of the Form
f(x) = a(x – h)2 + k.

22. Example
Graph g(x) = –4(x + 2)2 – 1. Find the vertex and axis of symmetry.