5.1 Modeling Data with Quadratic Functions

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5.1 Modeling Data with Quadratic Functions

• Objectives To identify quadratic functions and
  graphs and to model data with quadratic functions

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Critical Thinking

• Investigate
• As the side lengths of a square increase by 1,
  what happens to its perimeter and its area?
• Find a general rule to represent the relationship
  between any side length and its perimeter and
  area.

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Lets graph our results.
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Quadratic Functions
f(x) 3x2 - 7
y 2x2 3x 4
f(x) -10x2 3x
y (x 2)(x 3)
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Quadratic Function

• A function of degree two the largest exponent
  in the function is two
• Standard Form
• f(x) ax2 bx c
• Quadratic term Linear term
  Constant term

a ? 0
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Determine if the following is linear or
quadratic. Identify the quadratic, linear, and
constant terms.

• f(x) (x 2)(x 7) f(x) (x2 5x) x2

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Graphs of a Quadratic Function

• Parabolas
• Vertex(max/min)
• (2, 0)

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Identify the vertex and the axis of symmetry of
each parabola. Identify points corresponding to
P and Q.
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Finding a Quadratic Model

• Find a quadratic function that goes through (1,
  0), (2, -3), and (3, 10)

• By hand
• Substitute the values of x and y into
• y ax2 bx c and solve the system of
  equations with three variables

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Finding a Quadratic Model

• Using a graphing calculator
• Enter the data into calc
• STAT, Edit
• Find equation
• STAT, CALC, QuadReg, Enter

The table at the below shows the height of a
column of water as it drains from its container.
Model the data with a quadratic function. Use the
model to estimate the water level at 35 seconds.
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Homework

• Pg 237 1-16, 20-22, 32-36 even