Quadratic Graphing Basics

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Quadratic Graphing Basics
Lesson Created by Carol Keller

• College Algebra
• Local Objective 1-D
• GLE MA,AR,1,D,11

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Steps to graphing

• 1) Place the equation in standard form
• 2) Determine the a, b and c values
• 3) Find the equation for the Line of Symmetry
• 4) Determine the Vertex
• 5) Use the value of a to determine if the
  vertex is a maximum or a minimum
• 6) Obtain the y-intercept
• 7) Graph the parabola

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Place the equation in Standard form

• Standard Form for quadratics is

6 y x2 4x y x2 - 4x - 6
Example
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2) Determine the a, b and c values

• Once in standard form,

Determine the values of a, b and c
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When y x2 4x 6 a 1 b -4 c
-6 Why must we have the equation in standard
form???
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3) Find the equation for the Line of Symmetry

• Lines of symmetry are VERTICAL LINES
• The equation of a vertical line is always x
  some number
• Lines of Symmetry for quadratics are always x
  -b/2a

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When y x2 4x 6and a 1 b -4
c -6. the Line of Symmetry isx
-b -(-4) 2 2a 2(1)
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4) Determine the Vertex

• The vertex is always on the Line of Symmetryso
  that will be the x-coordinate of the vertex
  ordered pair.
• Place this value into the original function to
  determine the value of y.

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Get the Vertex
When y x2 4x 6 The line of symmetry
is x 2 The vertex will be (2, ???)
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y x2 4x 6
Since x 2 then y (2)2 4(2) 6
y 4 8 6
y -10
The vertex is (2, -10) !!!!!
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5) Use the value of a to determine if the
vertex is a maximum or a minimum

• If the value of a is positive the parabola
  will open upward and the vertex will be a
  minimum.
• If the value of a is negative the parabola will
  open downward and the vertex will be a maximum.

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On our earlier equation..
y x2 4x 6
The value of a is 1 so the parabola will open
upwards and the vertex will be a minimum.
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6) One other note!

• c will always be the y-axis intercept !!!!!
• This occurs because
• When y ax2 bx c
• Let x 0
• y a (0)2 b (0) c
• y c

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If y x2 4x 6 Then to find the y-intercept
let x 0. y (0)2- 4(0) 6 y -6 The
y-intercept is (0, -6)
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• Now that we know
• Line of Symmetry is x 2
• Vertex is (2,-10)
• y-intercept is (0,-6)
• Lets graph
• y x2 4x 6

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Practice! Practice! Practice!

• Graph the following
• 1) y x2 6x 1
• 2) y -x2 2x - 3