This document discusses quadratic functions and their graphs. It defines a quadratic function as having the form y = ax2 + bx + c. The graph of a quadratic function is a parabola, which has a vertex (lowest or highest point) and an axis of symmetry (vertical line through the vertex). It provides examples of graphing different quadratic functions using a graphing calculator and by hand, including how to find and plot the vertex and axis of symmetry.

1. Warm-up
 Evaluate when
x = -1, 0, and 2.
1. y = 2x2
- 3x + 5
2. y = 3(x - 7)2
- 6
3. y = -(x + 3)(2x - 7)

2. Graphing
Quadratic
Equations
5.1
p. 249

3. Quadratic Functions
 A quadratic function has the form
y = ax2
+ bx + c.

4. Quadratic Functions
 A quadratic function has the form
y = ax2
+ bx + c.
 The graph of a quadratic is called a parabola.

5. Quadratic Functions
 A quadratic function has the form
y = ax2
+ bx + c.
 The graph of a quadratic is called a parabola.
 The vertex is the lowest or highest point on the
parabola.

6. Quadratic Functions
 A quadratic function has the form
y = ax2
+ bx + c.
 The graph of a quadratic is called a parabola.
 The vertex is the lowest or highest point on the
parabola.
 The axis of symmetry is the vertical line going
through the vertex.

7. Quadratic Functions
 Graphing calculator:
y=1/2x2
, y=x2
, y=2x2
, y=3x2

8. Quadratic Functions
 The parabola opens up if a > 0.

9. Quadratic Functions
 The parabola opens up if a > 0.
 The parabola opens down if a < 0
(negative).

10. Quadratic Functions
 The x-coordinate of the vertex is -b/2a.

11. Quadratic Functions
 The axis of symmetry is the vertical line
x = - b
2a

12. Quadratic Functions
 The parabola is wider if a is a fraction.

13. Quadratic Functions
 The parabola is wider if a is a fraction.
 It is narrower if a is a whole number greater
than 1.

14. EX: y = 2x2
- 8x + 6
 Find the x-coordinate
of the vertex.

15. EX: y = 2x2
- 8x + 6
 Find the x-coordinate
of the vertex.
 Find the y-coordinate

16. EX: y = 2x2
- 8x + 6
1. Plot the vertex.

17. EX: y = 2x2
- 8x + 6
1. Plot the vertex.
2. Draw the axis of
symmetry.

18. EX: y = 2x2
- 8x + 6
1. Plot the vertex.
2. Draw the axis of
symmetry.
3. Plot 2 points on one
side

19. EX: y = 2x2
- 8x + 6
1. Plot the vertex.
2. Draw the axis of
symmetry.
3. Plot 2 points on one
side, and mirror them
on the other side.

20. EX: y = 2x2
- 8x + 6
1. Plot the vertex.
2. Draw the axis of
symmetry.
3. Plot 2 points on one
side, and mirror them
on the other side.
4. Draw a parabola
through the points.

21. Quadratic Functions
 If the equation is in the
form y=a(x-h)2
+k,
 The vertex is at (h, k)
 The axis of symmetry is
at x = h.

22. Quadratic Functions
 y = 2(x - 1)2
+ 3
Right 1
Up 3 vertex