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Notes 5.2

Expand Binomials Factor Sum/Diff of 2 Cubes Quadratic Equations Parent Standard Vertex Form : focus today. Notes 5.2. Notes 5.2 Pascal’s Triangle. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1.

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Notes 5.2

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  1. Expand Binomials • Factor Sum/Diff of 2 Cubes • Quadratic Equations • Parent • Standard • Vertex Form : focus today Notes 5.2

  2. Notes 5.2 Pascal’s Triangle 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 11 7 21 35 35 21 7 11 8 28 56 70 56 28 8 11 9 36 84 126 126 84 36 9 1 This slide and the next slide are informative but will not be tested! Use Pascal’s triangle to expand binomials!

  3. 11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 1

  4. Not tested

  5. Another type of factoring: Sum and Difference of 2 Cubes This type will require memorization to factor! Sum: a3+b3 Difference:a3-b3

  6. Examples Sum and Difference of 2 Cubes This type will require memorization to factor! Sum: x3+8 Difference:64y3-27

  7. Quadratic Equation Forms Parent Function Standard Form Vertex Form You have already been introduced to graphing Quadratics using the Parent Function and Vertex form (shifts). Today we will look deeper into the vertex form!

  8. Quadratic Functions: Parent Graph X Y -3 -2 -1 0 1 2 3 9 4 1 0 1 4 9

  9. Vertex form: y = (x – 2)2+1 Because a=1, there is no vertical stretch or shrink so the graph will be shaped identically to the parent Vertex: (h , k) = (2,1)

  10. Vertex form: y = 2(x – 3)2-1 K = -1 Shift (translate) down 1 x-3=0 solve … x=3 Positive “a” : opens up a>1 vertical stretch Shift (translate) 3 right h=3 a = 2 causes y-values to double the move from the parent! y (3,-1) Vertex: (h,k): Y=2(0-3)2-1 Y-intercept: • • (0,17) x=3 Axis of Symmetry: Parabola Shape of Graph: Are the solution/root/zeros real or imaginary? • • x •

  11. Vertex form: y = (x – 2)2 - 2 Positive “a” so parabola opens up. a=0.5 : compresses vertically K=-2 shift down 2. x-2=0 solve … x=2 shift 2 right. h = 2 a = .5 causes y-values to half the move from the parent! y (2,-2) Vertex (h,k): Y= (0-2)2-2 Y-intercept: (0,0) x=2 Axis of Symmetry: Parabola Shape of Graph: Are the solution/root/zeros real or imaginary? x

  12. Vertex form: y = -1(x + 3)2 - 4 a = -1 Neg. so opens down Neither stretch nor compress K = -4 shift down 4. X+3=0 solve … x= -3 Shift 3 left h = -3. a = 1 causes no y-values to stretch or compress from the parent! (-3,-4) Vertex (h,k): x Y = -1(0+3)2 - 4 Y-intercept: (0,-13) x=-3 Axis of Symmetry: Parabola Shape of Graph: Are the solution/root/zeros rational, irrational or imaginary? Imaginary because the graph never crosses the x-axis y

  13. Write the equation of a parabola in vertex form with a leading coefficient equal to – 4 and a vertex at ( – 5 , 3) Now convert the above equation to Standard form.

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