1. Parabola
Conic section

2. Quadratic Functions
The graph of a quadratic function is a parabola. y x
If the parabola opens up, the lowest point is called the vertex.
Vertex
If the parabola opens down, the vertex is the highest point.
Vertex

3. Standard Form y = ax2 + bx + c
The standard form of a quadratic function is y x
a = negative
a = positive
y = ax2 + bx + c
The parabola will open up when the a value is positive.
The parabola will open down when the a value is negative.

4. Graph the quadratic equation by factoring
Example
Graph the quadratic equation by factoring y x
1. y = x2 + 2x - 15
(x - 3) ( x + 5)
x = 3 , x =-5
Parabola opens upward

5. Example (x - 4) ( x - 2) x = 4 , x = 2 2. y = -(x2 - 6x + 8)
Graph the quadratic equation by factoring
2. y = -(x2 - 6x + 8) y x
(x - 4) ( x - 2)
x = 4 , x = 2
Parabola opens downward

6. Graphing with vertex y = ax2 + bx + c Formula in finding the vertex
y = substitute the value of x
(__, __) –4
Vertex = (__, __) x y

7. Example Find the vertex of y = -3x2 + 6x + 5 y = -3x2 + 6x + 5
Formula in finding the vertex
x = –b_ 2a
y = substitute the value of x
Find the vertex of y = -3x2 + 6x + 5
x = –b_ 2a
y = substitute the value of x
y = -3x2 + 6x + 5
x = –6
2(-3)
y = -3(1)2 + 6(1) + 5
x = –6 –6
y =
y = 8
x = 1
Vertex = (1, 8)

8. Graphing: y = ax2 + c 4. y = x2 – 2 5. y = x2 + 2 Vertex = (0, –2)

9. Graphing: y = ax2 + c 6. y = –x2 + 2 5. y = x2 + 2 Vertex = (0, 2)

10. Smaller coefficient = Wider parabola
Comparing Parabola
y - axis y x
Green y = 5x2
Purple y = ½x2
x - axis
Blue y = ¼ x2
Smaller coefficient = Wider parabola