Post on 26-Mar-2015
ParabolaConic section
Quadratic FunctionsThe graph of a quadratic function is a parabola.
If the parabola opens up, the lowest point is called the vertex.
If the parabola opens down, the vertex is the highest point.
y
x
Vertex
Vertex
Standard Form
y = ax2 + bx + c
The parabola will open down when the a value is negative.
The parabola will open up when the a value is positive.
y
x
The standard form of a quadratic function is
a = positive
a = negative
Example
Graph the quadratic equation by factoring
1. y = x2 + 2x - 15
y
x
(x - 3) ( x + 5)
Parabola opens
upward
x = 3 , x =-5
Example
Graph the quadratic equation by factoringy
x
Parabola opens
downward
2. y = -(x2 - 6x + 8)
(x - 4) ( x - 2)x = 4 , x = 2
Graphing with vertex
Vertex = (__, __)x y
(__, __)0 –4
Formula in finding the vertex
x = –b_ 2a
y = substitute the value of x
y = ax2 + bx + c
Example
Find the vertex of y = -3x2 + 6x
+ 5
Formula in finding the vertex
x = –b_ 2a
y = substitute the value of x
x = –b_ 2a
x = –6 2(-3)
x = –6 –6
x = 1
y = substitute the value of x
y = -3x2 + 6x + 5
y = -3(1)2 + 6(1) + 5
y = -3 + 6 + 5
y = 8 Vertex = (1, 8)
y
x
Graphing: y = ax2 + c4. y = x2 – 2
Vertex = (0, –2)
5. y = x2 + 2
Vertex = (0, 2)y
x
Graphing: y = ax2 + c5. y = x2 + 2
Vertex = (0, 2)y
x
6. y = –x2 + 2
Vertex = (0, 2)y
x
Comparing Parabolay
x x - axis
y - axis
Green y = 5x2
Purple y = ½x2
Blue y = ¼ x2
Smaller coefficient = Wider parabola