graphing quadratic functions a quadratic function is an equation of the form: y = ax 2 + bx + c
TRANSCRIPT
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Graphing Quadratic Functions
A quadratic function is an equation of the form:
y = ax2 + bx + c
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How long does a firework stay in the air?
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What is the hangtime of afootball?
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How does a satellite dish work?
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The graph of a quadratic function is called a parabola. It looks like a U or an upside down U.
4
2
-2
-4
-5 5
f x = x2-2x-34
2
-2
-4
-5 5
f x = -x2-2x +3
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Gallileo was the first to show that the path of an object thrown in space is a parabola.
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Graphing A Parabola
x y = x2 – 2x – 3 y
-2
-1
0
1
2
3
4
To graph a parabola we create a table of values and then plot the points. Lets Graph: y = x2 – 2x – 3
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y = x2 – 2x – 3
x y
-2 5
-1 0
0 -3
1 -4
2 -3
3 0
4 5
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Graphing A ParabolaLets Graph: y = -x2 + 2x + 1
x y = -x2 + 2x + 1 y
-2
-1
0
1
2
3
4
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y = -x2 + 2x +1
x y
-2 -7
-1 -2
0 1
1 2
2 1
3 -2
4 -7
y = -x2 + 2x + 1
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Vertex (Turning Point)
Quadratic Equation: y = ax2 + bx + c
The maximum or minimum point is called the vertex or turning point of the parabola.
If a is positive the graph looks like a smile. (Minimum)
If a is negative the graph looks like a frown. (Maximum)
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Axis of Symmetry
The line that divides a parabola directly in half is called its axis of symmetry.
The axis of symmetry and vertex (turning point) can be found using the equation:
a
bx
2
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Golden Gate Bridge
The cables that act as suspension are parabolas.
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3) y = -x2 + 4x – 1
Vertex is at:a
bx
2
y = -x2 + 4x – 1
x y
y = ax2 + bx + c
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y = -x2 + 4x – 1
x y
-1 -6
0 -1
1 2
2 3
3 2
4 -1
5 -6
Vertex?
Max or Min?
Axis of Symmetry?
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4) y = x2 – 2x – 8
Vertex is at:a
bx
2
y = x2 – 2x – 8
x y
y = ax2 + bx + c
![Page 19: Graphing Quadratic Functions A quadratic function is an equation of the form: y = ax 2 + bx + c](https://reader036.vdocuments.us/reader036/viewer/2022062500/5697c0221a28abf838cd3a4d/html5/thumbnails/19.jpg)
y = x2 – 2x – 8
x y
-2 0
-1 -5
0 -8
1 -9
2 -8
3 -5
4 0
Vertex?
Max or Min?
Axis of Symmetry?
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Homework
Graphing Parabolas Homework #1