Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the...
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Transcript of Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the...
![Page 1: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/1.jpg)
ParabolaConic section
![Page 2: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/2.jpg)
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
![Page 3: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/3.jpg)
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
![Page 4: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/4.jpg)
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
![Page 5: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/5.jpg)
Example
Graph the quadratic equation by factoringy
x
Parabola opens
downward
2. y = -(x2 - 6x + 8)
(x - 4) ( x - 2)x = 4 , x = 2
![Page 6: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/6.jpg)
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
![Page 7: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/7.jpg)
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)
![Page 8: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/8.jpg)
y
x
Graphing: y = ax2 + c4. y = x2 – 2
Vertex = (0, –2)
5. y = x2 + 2
Vertex = (0, 2)y
x
![Page 9: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/9.jpg)
Graphing: y = ax2 + c5. y = x2 + 2
Vertex = (0, 2)y
x
6. y = –x2 + 2
Vertex = (0, 2)y
x
![Page 10: Parabola Conic section. Quadratic Functions The graph of a quadratic function is a parabola. If the parabola opens up, the lowest point is called the.](https://reader033.fdocuments.in/reader033/viewer/2022061305/55144bf15503466d1a8b5d33/html5/thumbnails/10.jpg)
Comparing Parabolay
x x - axis
y - axis
Green y = 5x2
Purple y = ½x2
Blue y = ¼ x2
Smaller coefficient = Wider parabola