Math 101 – Chapter 6

STUDY SECTIONS 6.2, 6.3, 6.4 ON YOUR OWN.

YOU SHOULD HAVE STUDIED THIS MATERIAL IN A PRIOR CLASS.

Come to my office or go to the MathScienceCenter for help.

When I assign all odd numbered problems, start doing a few odd in each category (or group of problems). You want to be able to cover many topics. When you review again, do the ones you did not do before

Section 6.2 – Expanding and Factoring Polynomials

1)Multiplying (expanding) polynomials (1-6, 29-71 odd)

  1. Monomial by a polynomial
  2. Two binomials
  3. Binomial by a trinomial
  4. Two trinomials

2)Factoring polynomials by pulling out a common factor(7-16 odd)

3)Given a quadratic function in vertex form, write it in standard form(81-90 odd)

4)Evaluate quadratic functions given in standard form(97, 99, 101, 105, 107, 109)

  1. For a given number
  2. For a given expression

Section 6.3 – Factoring Quadratic Polynomials (1-80 odd)

1)Factoring quadratic polynomials ax^2 + bx +c

  1. a = 1
  2. a ≠ 1

2)Factoring a difference of two squares

3)The sum of squares is prime

4)Factoring combined

Follow these steps for factoring polynomials:

  1. First pull out all common factors (if possible)
  2. Then count the number of terms of the remaining polynomial.

- If it is a binomial, see if it’s a difference of squares.

- If it is a trinomial, use the methods discussed for trinomials.

Section 6.4 – Factoring Polynomials (Combined)

(1 – 19 odd, 35 – 73 odd, omit examples 2 and 3)

1) Follow these steps for factoring polynomials:

  1. First pull out all common factors (if possible)
  2. Then count the number of terms of the remaining polynomial.

- If it is a binomial, see if it’s a difference of squares

(If it is a sum of squares you can’t factor)

- If it is a trinomial, use the method discussed for trinomials.

Section 6.5 – Using Factoring to Solve Polynomial Equations

1)Solve quadratic equations by factoring(1-41 odd, 53-65 odd, omit examples 6 & 7)

  1. Steps:
  2. Set it = 0
  3. Factor
  4. Use the zero factor property
  5. Answer the problem
  6. Check answers by substituting back into the equation

2) Finding the x-intercepts of a quadratic function given in standard form(71-83 odd)

  1. Steps:
  2. Set f(x) = 0
  3. Factor
  4. Use the zero factor property
  5. Answer the problem
  6. Check answers by using a graph.
  7. Enter function in Y=
  8. Graph
  9. 2nd CALC

select 2:zero

3)What is the possible number of x-intercepts of a quadratic function?

Sketch graphs for the different possibilities.

4)Given a quadratic function in standard form, answer the two basic problems(91-98 all)

  1. Find f(#), (i.e. given x, find y)
  2. Given f(x), find x (i.e., given y, find x)

5)Given the graph of a quadratic function, answer the two basic problems(99-106 all)

  1. Find f(#), (i.e. given x, find y)
  2. Given f(x), find x (i.e., given y, find x)

6)Given the table of a quadratic function, answer the two basic problems(107-114 all)

  1. Find f(#), (i.e. given x, find y)
  2. Given f(x), find x (i.e., given y, find x)

Section 6.6 – Sketching Graphs of Quadratic functions in Standard Form

1)Given the equation of a parabola in the standard form.(17-35 odd)

a)Find the x-coordinate of the vertex (Use the formula x = -b/2a)

b)Find the y-coordinate of the vertex

2)Solve word problems involving quadratic functions.

Questions are dealing with

a)Evaluation

b)Finding x-intercepts

c)Finding the coordinates of the vertex

Section 6.1 – Quadratic Functions in Vertex Form

Given a quadratic function in vertex form(1 – 24 odd)

F(x) = a (x-h)^2 + k

2)Write the values of the constants a, h, k and explain the transformations that took place

  1. Vertical stretch / compression
  2. X-reflection (opens down)
  3. Vertical translation (up-down shifts)
  4. Horizontal translation (left-right shifts)

3)Sketch the graph of quadratic functions given in the vertex form.

  1. By hand
  2. Using the calculator (indicate window values)

4)Give the coordinates of the vertex.

5)Give the domain.

6)Give the range.

Section 11.4 – Complex Numbers (1-11 odd)

1)Evaluating square roots of negative numbers

2)Simplifying expressions and writing answers in the form a + bi

Section 7.1 – Solving Quadratic Equations by extracting Square

Roots (1 – 64 odd)

1)Simplifying radicals by using the distributive properties with respect to a product and with respect to a quotient.

2)Simplifying radicals by rationalizing the denominator

3)Solving quadratic equations of the form x^2 = k (square root property)

4)Solving quadratic equations by using the square root property

  1. Isolate the quadratic quantity
  2. Use the square root property to solve
  3. Simplify solutions

5)Finding the x-intercept of quadratic functions by using the square root property

Section 7.3 – Solving Quadratic Equations by Using the

Quadratic Formula

(1-78 odd, 83, 85, also do some from Section 11.4 57 – 75 odd)

1)Using the quadratic formula to solve quadratic equations

2)Using the method of your choice to solve quadratic equations

Section 7.6 – Modeling with Quadratic Functions (1 – 15 odd)

1)Sketching scatter diagrams and finding the quadratic model that fits the data.

2)Make estimates and predictions using a quadratic model.

3)Interpreting results within the context of the problem.

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