7'2 Notes Equivalent Quadratic Forms

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7.2 Notes Equivalent Quadratic Forms

• Quadratic is a 2nd degree polynomial
• There are 3 forms of a Quadratic function

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General Form

• The general form tells you the y intercept
• The y intercept is where the graph crosses the
  y- axis
• The y intercept is (0,c)

3
Vertex Form

• The vertex form tells you the vertex (h,k)
  note you take the opposite of h
• That is the maximum or minimum of the parabola
• If a is positive the parabola opens up and you
  have a minimum
• If a is negative the parabola opens down and you
  have a maximum

4
Factored form

• The factored forms tells you the x-intercepts,
  roots or zeros
• That is where the graph crosses the x-axis
• Set each factor equal to zero and solve
• The roots will be (r1,0) and (r2 ,0)

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Example 1 Given

• What form is it in?
• Find the vertex
• Convert to general form and state the y-intercept

Vertex form
Vertex (1,-4)
Distribute (x-1)(x-1) 4 x2
1x -1x 1 4 y x2 2x -
3 Y-intercept is (0,-3)
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Ex2 Given

• Find the zeros
• What does this mean on a graph?

Set each factor equal to zero and solve x
5.6 0 x 3.1 0 x 5.6 x
-3.1 zeros (5.6, 0) and (-3.1 ,0)
This is where it crosses the x-axis
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Example a) state the vertex,
b) determine if its a max or min c) write
the equation in vertex form d) write the
equation in factored form
Sketch the graph ?

• Blue graph
• a) (-4,5)
• b) its a minimum (opens up so a is positive)
• y (x 4)2 5
• y (x1.8)(x6.2) factored form is
  (x-r1)(x-r2) so you take the opposite of the
  roots
• Try the red graph on your own

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The height of an object rising or falling under
the influence of gravity
x time in seconds y objects height from the
ground in feet a half the downward acceleration
due to gravity on
Earth a -4.9m/s2 or -16ft/s2 V0 initial upward
velocity of the object in meters or feet per
second S0 initial height of the object in
meters or feet
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A stop watch records that when Wyatt jumps in the
air he leaves the ground at 0.25 seconds and
lands at 0.83 seconds.

• Sketch a graph of what is happening
• Write an equation in factored form what does
  each number mean?
• Lets say that Wyatt reaches a height of 1.32 feet
  at 0.54 seconds, write an equation to model that.
  (What form should we use?)
• Write an equation in standard form, what does
  each number mean, do they all make sense?

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Summary

• Class work 7.2 wsht
• Homework 7.2 page 372-3
  1-5,7,8ab,9ab,11,12,16