chapter 6 quadratic...
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Math 1201: Linear Functions
Math 2201: Quadratic Functions
Math 3201: Cubic, Quartic, Quintic Functions
is the linear term 3 is the leading coefficient
-4 is the constant term
CHAPTER 6 Quadratic Functions
Section 6.1: Exploring Quadratic Relations
The path a ball travels gives a special “U” shape called a “parabola.”
Quadratic Functions:
the shape is a parabola
the simplest quadratic function is
(The word quadratic comes from the word quadratum, a Latin word meaning square.)
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How to create a quadratic function?
What do you notice about the degree (highest exponent of the variable) of the function?
the result of multiplying two linear functions:
Example:
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Which of the following functions are quadratic?
i) ii)
iii) iv)
v) vi)
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Characteristics of the basic quadratic function .
x y
-2
-1
0
1
2
Create table of values
What is the vertex?__________
What is the x-intercept?__________
What is the y-intercept?__________
What is the domain and range? Domain:__________
Range:__________
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Direction of Opening: a parabola can open up or down.
When the graph opens up the vertex is the lowest point on the graph and the y-coordinate of the vertex is the minimum value of the function.
When the graph opens down the vertex is the highest point on the graph and the y-coordinate of the vertex is the maximum value of the function.
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Axis of Symmetry
• The parabola is symmetric about a vertical line called the axis of symmetry
• This lines divides the graph into two equal parts.
• It is the mirror image
• It intersects the parabola at the vertex
The equation of the axis of symmetry corresponds to the x-coordinate of the vertex
Another Example:
• What is the equation of the axis of symmetry for the above graph?
What is the equation of the axis of symmetry?
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Why are quadratic relations also quadratic functions?
> For every value of x there is only one value for y.
> It passes the vertical line test!
Think about:
Relation vs Function
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Standard Form of A Quadratic Function:
whereTerminology:
• = the quadratic term
• = the coefficient of the quadratic term
Example:
term and 3 is the
term and -4 is the
y = 3x2- 4x + 1
3x2
-4x
1
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Part A: The Effect of a in on the graph of
Standard Form of A Quadratic Function:
Investigate the parameters , and
1) What happens to the direction of the opening of the quadratic if or ?
2) If the quadratic opens upward, is the vertex a maximum or minimum point?
3) If the quadratic opens downward, is the vertex a maximum or minimum point?
4) Is the shape of the parabola effected by the parameter ? Are some graphs wider or narrower compared to the original ?
5) What happens on the graph when ?
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Part B. The Effect of on the graph of
• b changes the location of the:__________and the ___________
What is the effect of parameter in on the graph of ?
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Part C. The Effect of c on the graph of
· the c-value changes the _________________
What is the effect of parameter in on the graph of ?
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Work Sample 6.1: pg. 324 #s 1a-f, 2a-e, 5a-d
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