Today in Pre-Calculus

1
Today in Pre-Calculus

• Go over homework
• Notes
• Quadratic Functions
• Homework

2
Quadratic Functions

• Standard form f(x) ax2 bx c
• Roots (zeroes or x-intercepts) are found by
  factoring or using quadratic formula
• Vertex form f(x) a (x h)2 k
• Vertex of the parabola (h, k)
• Axis of symmetry x h

3
Quadratic Functions

• To convert from standard form to vertex form
  using algebra Complete the square.
• Example y 2x2 16x 31
• y 2(x2 8x) 31 Factor a only
  from x2 and x
• y 2(x2 8x 16)-32 31 Divide new b by 2
  and square it, must also
  multiply by a and subtract to
  keep equation true.
• y 2(x 4)2 1 Factor and simplify
• Parabola with vertex (-4, -1) and axis of
  symmetry x -4.

4
Practice

• Example Use algebra to describe y 3x2 18x
  17
• y 3(x2 6x) 17 Factor a from
  x2 and x
• y 3(x2 6x 9) 27 17 Divide new b by 2
  and square it, must also
  multiply by a and subtract to
  keep equation true.
• y 3(x 3)2 44 Factor and simplify
• Parabola with vertex (3, -44) and axis of
  symmetry x 3.

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Formulas for h and k

• Example y 2x2 16x 31
• k 31 (2)(-4)2 or k 2(-4)2
  16(-4) 31
• k -1
• Vertex (-4, -1)

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Practice

• Use the formulas to find the vertex of y 3x2
  5x 4

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Example

• Write the equation for a parabola with a vertex
  (-1,2) that goes through (6,100).
• start with vertex form y a(x 1)2 2
• substitute point 100 a(6 1)2
  2
• 98 49a
• a 2
• y 2(x 1)2 2

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Homework

• Pg. 182 24-30 even, 36-42 even
• Bring books tomorrow