Transcript Quadratic Functions - Reeds Spring High School

Quadratic
Functions
Objectives:
Graph a Quadratic Function
using Transformations
Identify the Vertex and Axis of
Symmetry of a Quadratic
Function
Graph a Quadratic Function
using its Vertex, Axis and
Intercepts
Quadratic Function
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A function that is
defined by a 2nd
degree polynomial in
one variable. The
domain is  ,  
f  x   ax 2  bx  c
where a, b, and c are
real numbers and a  0
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Standard form shows
the vertex, the axis of
symmetry and whether
it opens up or down.
2
f  x  a  x  h  k; a  0
Vertex: h, k 
Axis of Symmetry:x  h
Opens up:a  0
Opens down:a  0
Graphing Quadratic Function with
2
f
x

a
x

h
Equations in Standard form      k
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1. Determine whether the parabola opens
upward  a  0  or downward  a  0 
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2. Determine the vertex of the parabola
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3. Find the x-intercepts by solving f  x   0
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4. Find the y-intercept by computing f  0 
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 h, k 
5. Plot the intercepts, the vertex, and additional
points as necessary. Connect these points with a
smooth curve that is shaped like a cup.
Graph the quadratic function
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1.
f  x   2  x  3  8
2
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2.
g  x    x  3  1
2
Graphing Quadratic Function with
Equations in the form f  x   ax 2  bx  c
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1. Determine whether the parabola opens
upward  a  0  or downward  a  0 
 b
 b 

,
f
2. Determine the vertex of the parabola 
 
 2a  2a  
b
3. Find the axis of symmetry x  
2a
4. Find the y-intercept  0,c  and the x-intercepts f  x   0
5. Plot the vertex, the axis of symmetry, y-intercept
and its symmetry point. Connect these points with
a smooth curve that is shaped like a cup.
Graph each quadratic function by determining whether its
graph opens up or down and by finding its vertex, axis of
symmetry, y-intercept, and x-intercepts (if any). Determine
the domain and the range of the function. Determine where
the function is increasing and decreasing.
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3.
f  x   x2  2x  8
Graph each quadratic function by determining whether its
graph opens up or down and by finding its vertex, axis of
symmetry, y-intercept, and x-intercepts (if any). Determine
the domain and the range of the function. Determine where
the function is increasing and decreasing.
• 4.
f  x   3x 2  6 x
Determine the quadratic function whose
graph is given.
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5.
Minimum and Maximum of Quadratic
Functions
If a  0 , then f has a minimum that occurs at
b . This minimum value is  b 
x
f  
2a
 2a 
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If a  0 , then f has a maximum that occurs at
b
b
x   . The maximum value is f   
2a
 2a 
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6. Determine, without graphing, whether the
given quadratic function has a max or min value
and find it
f  x   2 x 2  12 x  3