Summary of 3 forms of quadratic function

1
Summary of 3 forms of quadratic function

• NOTE The a in each form is EXACTLY the same
  number. It is the only value that CHANGES the
  SHAPE of the curve. It is the only non-rigid
  transformation.
• The other numbers change the location of the
  curve. They are all RIGID transformations.

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Common for all 3 forms

• Standard f(x) ax2 bx c
• Vertex f(x) a(x h)2 k
• Intercept f(x) a(x p)(x q)
• The a in each form is EXACTLY the same number.
  It is the only value that CHANGES the SHAPE of
  the curve. It is the only non-rigid
  transformation.
• The other numbers change the location of the
  curve. They are all RIGID transformations.

3
Standard Form of the Quadratic

• Stretch Factor Rigid VERTICAL Shift
  (y-intercept)
• y ax2 bx c
• Axis of Symmetry is
• Find y part of vertex by substituting the axis
  of symmetry into the equation for x
• Use the x and y to change to vertex form
• Factor to change to intercept form

4
Vertex Form of the Quadratic(can find the vertex
easily at (h, k))

• From parent curve of y x2
• Stretch factor Rigid Shift VERTICAL
  amount
• y a(x h)2 k
• Rigid Shift HORIZONTAL amount
• Distribute to change to standard form

5
Intercept Form of the Quadratic(can find the
intercepts easily)

• Stretch Factor
• y a(x p)(x q)
• The x-intercepts are at (p, 0) and (q, 0)
• Axis of Symmetry is located in the middle of the
  intercepts, so it is
• Find y part of vertex by substituting the axis
  of symmetry into the equation for x
• Distribute to change to standard form