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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Quadratic Functions andModels
Quadratic Functions and Models
Quadratic Function
Domain All real numbers
Range y ≥ 0Passes thru (0, 0)
Parent Function
The graph of a quadraticfunction is called aparabola.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
GRAPHING A QUADRATIC FUNCTION
A quadratic function has theform f(x) = ax 2 + bx + c ,where a
0.
The graph of the quadraticfunction f(x) = ax2 + bx + cwhere a 0,
is the set of points(x, y) that satisfy the equationy = ax 2 + bx +
c.
GRAPHING A QUADRATIC FUNCTION
The graph is “U-shaped” and is calleda parabola.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
GRAPHING A QUADRATIC FUNCTION
The highest or lowest point on theparabola is called the
vertex.
GRAPHING A QUADRATIC FUNCTION
In general, the axis of symmetry forthe parabola is the vertical
linethrough the vertex.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
GRAPHING A QUADRATIC FUNCTION
These are the graphs of y = x2and y =-x2.
GRAPHING A QUADRATIC FUNCTION
The origin is the vertex for bothgraphs.
The origin is the lowest point on thegraph of y = x2, and the
highest pointon the graph of y =-x2.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
GRAPHING A QUADRATIC FUNCTION
The y-axis is the axis of symmetryfor both graphs.
GRAPHING A QUADRATIC FUNCTION
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Standard Form
Quadratic Functionc = y-intercept
a > 0 a < 0 Axis of Symmetry:
Vertex:
Quadratic Function
a > 0 a < 0
Axis of Symmetry:
Vertex:
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
THE GRAPH OF A QUADRATIC FUNCTIONGRAPHING A QUADRATIC
FUNCTION
If b 2 – 4ac > 0,the graph has two x-intercepts.
If b2 – 4ac = 0,the graph has one x-intercept.
If b2 – 4ac < 0,the graph has no x-intercepts.
Quadratic FunctionGraphing Quadratic Functions in Standard
Form
1) Determine the axis of symmetry.2) Find the vertex, V.3) Setup
a table and pick 2 points to the left and 2
points to the right of the x-value of the vertex.4) Connect the
points and draw a smooth curve.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Graphing Quadratic Functions in Standard Form
1) Determine the axis of symmetry.
2) Find the vertex.
3) Setup a table and pick 2 points to the left and 2points to
the right of the x-value of the vertex.
Ex) Graph the given function using a table.
x f(x)
3 -1
Graphing Quadratic Functions in Standard Form
4) Connect the points and draw a smooth curve.
Ex) Graph the given function using a table.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Finding Minimum and Maximum Values
The maximum or minimum value is they-value of the vertex.
Quadratic FunctionIntercept/Factored Form
b and c are calledzeros or x-intercepts
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Represent the quadratic function ingeneral form. Identify a, b,
and c.
Represent the quadratic function ingeneral form. Identify a, b,
and c.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Represent the quadratic function ingeneral form. Identify a, b,
and c.
Example: Find the vertex, AoS, max/min, zeros, and tell
whether concave up or concave down.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Example: Find the vertex, AoS, max/min, zeros, and tell
whether concave up or concave down.
These are the solutions.What are the x-intercepts?
Example: Find the vertex, AoS, max/min, zeros, and tell
whether concave up or concave down.
These are the solutions.What are the x-intercepts?
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Example Find the vertex, AoS, max/min, zeros, and tell
whether concave up or concave down.
Example: Find the vertex, AoS, max/min, zeros, and tell
whether concave up or concave down.
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Quadratic Functions and Models
RNBriones Mt. Diablo High School
Example: Find the vertex, AoS, max/min, zeros, and tell
whether concave up or concave down.
