Advanced Algebra 1

Final Exam (D)

Tuesday, 7/15 @9:55am

Final Exam (H)

Tuesday, 7/19 @9:55am

Unit 7: Polynomials &

Rational Functions

Solving and Graphing  a Polynomial Function Notes

Solving and Graphing  a Polynomial Function Video

#1 in the Packet

#5 in the Really Difficult Packet

Unit 6: Exponential Functions &

Logarithmic Functions

Open-Note Quarter-Final Exams 

D-Period: Wednesday (3/20)

H-Period: Monday (3/18)

List of Stuff to Know & Apply with Practice Problems

1. Multiply ‘a’ and ‘c’.
2. Identify the two numbers whose product is the result of step 1 result and a sum of ‘b’.
3. Divide the step 2 results by ‘a’.
4. Reduce fractions if possible.
5. Insert parentheses, symbols, and ‘x’s.
6. Move denominator in front of ‘x’s.

GCF Factoring

Factoring a Trinomial

Factoring Completely

Solving Quadratics

Solving Using Square Roots

 Solving Using Quadratic Formula

Worksheets & Homework 

Helpful Resources

Vertex Form of a Quadratic

If 'a' is positive, the U opens upward.  If 'a' is negative, the U opens downward.  'a' acts like slope (rate-of-change).

The number next to the x, tells you how many units the vertex shifts to the left or right (in the opposite direction).

The number at the end, tells you how many units the vertex shifts up or down (in that direction).

To find the y-intercept, plug 0 in for x (and solve for y).

A symmetric point exists the same distance from the axis of symmetry (on the other side).

Standard Form of a Quadratic

If 'a' is positive, the U opens upward.  If 'a' is negative, the U opens downward.  'a' acts like slope (rate-of-change).

'c' is the y-intercept.

x-coordinate of the Vertex (& Equation of the axis of symmetry) x = -b/2a

y-coordinate of the Vertex: plug x into equation.

A symmetric point exists the same distance from the axis of symmetry (on the other side).

Intercept Form of a Quadratic

If 'a' is positive, the U opens upward.  If 'a' is negative, the U opens downward.  'a' acts like slope (rate-of-change).

The x-intercepts are p & q.

To find the y-intercept, plug 0 in for x (and solve for y)

x-coordinate of the Vertex (& Equation of Axis of Symmetry) x = (p + q)/2

y-coordinate of the Vertex: plug x into equation.

A symmetric point exists the same distance from the axis of symmetry (on the other side).

Worksheets & Homework

Cramer’s Rule for 2x2

Part 1 (Calculating OD)

1.                  Extract Coefficients (Leaving out the Constant Matrix)

2.                  Calculate Determinant of Original Matrix

Part 2 (Solving for x)

3.                  Replace the 1^st column of the coefficient matrix with the constant matrix.

4.                  Calculate the determinant of new matrix & divide by OD.

Part 3 (Solving for y)

5.                  Replace the 2^nd column of the coefficient matrix with the constant matrix.

6.                  Calculate the determinant of new matrix & divide by OD.

Part 4 (Check your solutions)

7.                  To check x and y, substitute 51 in for x and 30 in for y.

Cramer’s Rule for 3x3

Part 1 (Calculating OD)

1.                  Extract Coefficients (Leaving out the Constant Matrix)

2.                  Calculate Determinant of Original Matrix

Part 2 (Solving for x)

3.                  Replace the 1^st column of the coefficient matrix with the constant matrix.

4.                  Calculate the determinant of new matrix & divide by OD.

Part 3 (Solving for y)

5.                  Replace the 2^nd column of the coefficient matrix with the constant matrix.

6.                  Calculate the determinant of new matrix & divide by OD.

Part 4 (Solving for z)

7.                  Replace the 3^rd column of the coefficient matrix with the constant matrix.

8.                  Calculate the determinant of new matrix & divide by OD.

Part 5 (Check your solutions)

9.                  To check x, y, and z substitute 2.6 in for x, 2.2 in for y and 0.2 in for z.

Powerpoints & Other Helpful Resources

Miscellaneous Notes

Solving Systems using Linear Combination

Solving Systems by Substitution

Solving Systems by Graphing

CW/HW Assignments

Miscellaneous Notes

Graphing Absolute Value Functions

If the number in front is positive, the V opens upward. 

If the number in front is negative, the V opens downward. 

The number in front also acts like slope.  It gets plotted from our vertex to the left/right.  

The number next to the x, tells you how many units the V-shifts to the left or right (in the opposite direction)

The number at the end, tells you how many units the V-shifts up or down (in the that direction)

1. Plot the y-intercept
2. Plot the slope
3. Draw the line (as a Solid or Dotted line)
4. Pick a point (x,y) and plug it in.

• If true, shade the side that contains your (x,y).
• If false, shade the side that doesn't contain your (x,y).

CW/HW Assignments

Period D: Friday

Period H: Thursday

Miscellaneous Notes

Classwork/Homework

 Review Questions

 Review Answers

Miscellaneous Notes

Graphing y=mx+b 

1. Plot y-intercept (b).
2. Plot slope (m) from y-intercept repeatedly.
3. Draw the line that goes through the points.
   

Graphing ax+by=c

1. Plug 0 in for x, solve for y, and plot (0, y).
   
2. Plug 0 in for y, solve for x, and plot (x, 0).
3. Draw the line that goes through the points.

Classwork/Homework

HW #6

Complete Slope Packet

Miscellaneous Notes

Solving Absolute Value Equations

1.  Bring the same symbol (=) to the other side of the absolute value expression.

2.  Bring the opposite number (-) to the other side of the absolute value  expression.

3.  Split into two equations and solve to get 2 solutions.

Order of Operations

Parenthesis

Exponents

Multiplication or Division

Addition or Subtraction

Things to Remember

When adding or subtracting "like terms",
the coefficient changes.
When multiplying or dividing "like terms",
the exponent changes.

Classwork/Homework

HW #5: H-Period

Complete

Solving Equations Packet

HW #4: D-Period

Solving Equations Packet: a-c, #1-6