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Name: __________________________________________ Algebra II / Trigonometry

Unit 3Quadratics

Unit 3: Quadratics

Date Topic Classwork Pages

Homework Pages

Day 1 – Solving Quadratic Equations by Factoring 3-4 5-8

Day 2 – Solving Quadratic Inequalities by Factoring 9-10 11-13

Day 3 – Solving Rational Equations / Check Roots 14-15 16-18

Day 4 – Solving Rational Inequalities (graphically only) 19-21 22-24

Day 5 – Completing the Square to find the Roots (1) 25-27 28-30

Day 6 – Completing the Square to find the Roots (2) 31-33 34-35

Day 7 – QUIZ / Using the Quadratic Formula to find the Roots of a Polynomial (Note: Quiz will include Days 1-5 only)

36-37 38-39

Day 8 – Finding the Product and Sum of the Roots, and Finding the Equation given the Roots

40-41 42-43

Day 9 – Given One Root, Find the Second Root of an Equation 44-45 46-48

Day 10 – Solving Higher Degree Polynomial Equations Using Factor By Grouping

49-51 52-53

Day 11 – Solving Higher Degree Polynomial Equations 54-55 56-57

Day 12 – Solving Higher Degree Polynomial Equations / Graphically

58-59 60

Day 13 – Systems of equations / inequalities algebraically 61-63 64-66

Day 14 – Systems of equations / inequalities graphically** Don’t forget your index cards tomorrow **

67-69 70-72

Day 15 – Review 73-75 Study!

Day 16 – TEST

Day 1 – Solving Quadratic Equations by FactoringSteps to Solving Quadratic Equations by Factoring:

1.) Simplify the equation. (For example, distribute)2.) Set the equation equal to zero. (In standard form: , where )3.) Factor.4.) Set each factor to zero.5.) Solve each resulting equation for x.

Directions: Solve each quadratic equation.1.) 2.)

3.) 4.)

Practice ProblemsDirections: Solve each quadratic equation.5.) 6.)

7.) 8.)

Day 1 – Solving Quadratic Equations by FactoringHOMEWORK

**Complete any Practice Problems from class work that have not been completed**Directions: Solve each quadratic equation.1.) 2.)

3.) 4.)

5.) 6.)

7.) 8.)

9.) 10.)

11.) The width of a rectangle is 12 feet less than the length. The area of the rectangle is 28 square feet. Find the dimensions of the rectangle.

Review12.) Express the sum is simplest radical form:

13.) Express in simplest form:

14.) Write with a rational denominator in simplest radical form.

Day 2 – Solving Quadratic Inequalities by FactoringDo Now: (Questions 1 & 2)1.) The solution set of is (1) {2, 4} (3) {2, -4} (2) {-2, 4} (4) {-2, -4}

2.) Find the roots of the given equation:

Steps to Solving Quadratic Inequalities by Factoring:1.) Simplify the inequality. (For example, distribute)2.) Move each term to one side of the inequality with zero on the other side.(Remember you want )3.) Factor.4.) Set each factor to zero.5.) Solve each resulting equation for x.6.) Graph or write the solution set.

a.) If the inequality sign makes a “C” for connect the solution set is all connected together.b.) If the inequality sign does NOT make a “C” the solution set is NOT connected and the word

“OR” is used to write the solution.Directions: Write the solution set and graph each quadratic inequality.3.) 4.)

5.) 6.)

Practice ProblemsDirections: Write the solution set and graph each quadratic inequality.9.) 10.)

Day 2 – Solving Quadratic Inequalities by FactoringHOMEWORK

**Complete any Practice Problems from class work that have not been completed**Directions: Write the solution set and graph each quadratic inequality.1.) 2.)

3.) 4.)

5.) 6.)

Review

7.) Simplify:

8.) Perform the indicated operation and simplify:

9.) The length of Bill’s rectangular garden is 2 yards more than four times the width. The area of the

garden is 30 square yards. What are the dimensions of the garden?

Day 3 – Solving Rational Equations / Check RootsDo Now: (Questions 1 & 2)1.) Solve for x: (1) or (3) or

(2) (4)

2.) What is the graph of the solution set of ?(1)

(2)

(3)

(4)

Steps to Solving Rational Equations:1. Multiple each term on both sides of the equation by the least common denominator.2. Cancel out the denominators.3. Solve the resulting equation.4. Check to make sure that the solutions do not make the original equation undefined.

Directions: Solve each equation.

3.) 4.)

-1 3

-1 3

-1 3

-1 3

5.) 6.)

Practice ProblemsDirections: Solve each equation.

7.) 8.)

Day 3 – Solving Rational Equations / Check RootsHOMEWORK

**Complete any Practice Problems from class work that have not been completed**Directions: Solve each equation.

1.) 2.)

3.) 4.)

5.) 6.)

Review7.) Express in simplest form:

8.) Simplify:

9.) Simplify: 10.) Solve for b:

Day 4 – Solving Rational InequalitiesDo Now: (Question 1)

1.) Solve for x:

Steps to Solving Rational Inequalities:1. Move all terms onto the left side of the inequality using either addition or subtraction. 2. Find a common denominator, and combine all fractions into a single term.3. Find the “critical values” by setting the numerator = 0 and solve, and set the denominator = 0 and

solve. This will give you the x-intercepts or the asymptotes. (Note: If the denominator is an integer, then there is no critical value for the denominator.)

4. Graph the inequality as an equation in y=. (Wrap the numerator, wrap the denominator for each term.)

5. Write your solution. If the original inequality is >0, then look for the solution where the graph is above the x-axis. If the original inequality is <0, then look for the solution where the graph is below the x-axis.

Directions: Solve each inequality.

2.)

3.)

4.)

Day 4 – Solving Rational InequalitiesHOMEWORK

Directions: Solve each inequality.

1.)

2.)

3.)

4.)

Review

7.) Solve for x: 8.) What is the solution set for the equation:

9.) Simplify: 10.) Express with a rational denominator in simplest

radical form:

Day 5 – Completing the Square to find the Roots (1)Do Now: (Questions 1 & 3)

1.) Solve the inequality:

(1) (3)

(2) (4)

2.) Solve for x:

(1) (3)

(2) (4)

3.) Standard form of a quadratic equation: Find given the quadratic equation = 0.

Steps for Completing the Square (when a = 1)1.) Rearrange the equation to be in the form 2.) Rewrite the equation with a blank space at the end of each side to insert the result from step 3.

Ex) ax2 + bx + _______ = c + _____3.) Divide b by 2, and then square the result.

4.) Fill in (the number from step #3) on both sides of the equation.

5.) Factor the left side. (Write as a perfect square in factored form.)6.) Take the square root of each side of the equation. (Don’t forget both positive and negative.)7.) Solve for x. 8.) Simplify (if possible).Directions: Solve for x, in simplest radical form, if possible.4.)

5.)

6.) Solve for the positive root, to the nearest tenth.

Practice Problems

Directions: Solve for x, in simplest radical form, if possible.7.)

8.)

Day 5 – Completing the Square to find the Roots (1)HOMEWORK

**Complete any Practice Problems from class work that have not been completed**Directions: Solve for x, in simplest radical form, if possible.1.) 2.)

3.) 4.)

5.) 6.)

7.) 8.)

Review

9.) Simplify:10.) Solve for x:

Day 6 – Completing the Square to find the Roots (2)Do Now: (Questions 1 & 2)1.) What number must be added to both sides of

the equation to solve it by completing the square?

(1) 225 (3) 6.25 (2) 25 (4) 5

2.) Solve by completing the square, expressing the result in simplest form.

Steps for Completing the Square when a 1 1.) Rearrange the equation to be in the form

*NOTE: If , divide each term of the equation by to make .2.) Rewrite the equation with a blank space at the end of each side to insert the result from step 3.

Ex) ax2 + bx + _______ = c + _____3.) Divide b by 2, and then square the result.

4.) Fill in (the number from step #2) on both sides of the equation.

5.) Factor the left side. (Write as a perfect square in factored form.)6.) Take the square root of each side of the equation. (Don’t forget both positive and negative.)7.) Solve for x. 8.) Simplify (if possible)

Directions: Solve for x, in simplest radical form, if possible.3.)

4.)

5.)

6.)

Practice Problems7.)

Day 6 – Completing the Square to find the Roots (2)HOMEWORK

**Complete any Practice Problems from class work that have not been completed**Directions: Solve for x, in simplest radical form, if possible.1.) 2.)

3.) 4.)

Review5.) Perform the indicated operation. Simplify your answer to lowest terms.

6.) Rationalize the denominator in simplest form:

Day 7 – Using the Quadratic Formula to find the Roots of a PolynomialDo Now: QUIZSteps for Solving using the Quadratic Formula1.) Rearrange the equation to be in the form .

2.) Substitute the appropriate values for a, b, and c into the formula:

3.) Simplify the radical expression as much as possible, or round the answer as instructed.Directions: Use the quadratic formula to find the roots of each equation, in simplest form.1.)

2.)

3.) Use the quadratic formula to find the roots of to the nearest tenth.

Day 7 – Using the Quadratic Formula to find the Roots of a PolynomialHOMEWORK

Directions: Use the quadratic formula to find the roots, in simplest radical form if possible.1.) 2.)

3.) 4.)

Review5.) Perform the indicated operation. Simplify your answer to lowest terms.

6.) Rationalize the denominator in simplest form:

Day 8 – Finding the Product and Sum of the Roots, and Finding the Equation given the RootsDo Now: (Question 1)1.) Solve this equation for x. An algebraic solution is required. Express the answer in simplest radical

form:

Steps for Finding the Sum and Product of the RootsRearrange the equation to be in the standard form

Sum = , Product =

Directions: For each equation, solve for the sum and product of the roots.2.) 3.)

4.) 5.)

Steps for Writing the Quadratic Equation When Given the Roots of the Equation1.) Solve for the sum and the product of the roots2.) Fill the sum and product of the roots into the standard form of the equation:

3.) If necessary, multiply all terms by the greatest common denominator.

Directions: Write a quadratic equation with integer coefficients for each pair of roots.6.) 4, 7 7.) –3, 3

8.) 9.) Write a quadratic equation with integer coefficients when given one root :

Day 8 – Finding the Product and Sum of the Roots, and Finding the Equation given the RootsHOMEWORK

Directions: Without solving each equation, find the sum and product of the roots.1.) 2.)

3.) 4.)

Directions: Write a quadratic equation with integer coefficients for each pair of roots.5.) 2, 5

6.)

Directions: Given one of the roots, write a quadratic equation with integer coefficients.7.) 8.)

Review

9.) Write as an equivalent fraction with a rational denominator.

10.) Simplify the rational expression and list all values of m for which the fraction is undefined.

Day 9 – Given One Root, Find the Second Root of an EquationDo Now: (Questions 1 & 2)1.) For which equation does the sum of the roots

equal and the product of the roots equal –2?

(1) (2) (3) (4)

2.) Find the values of b and c in the following equation if the roots of the equation are :

Steps for Finding the Second Root When One is GivenMethod 1:1.) Use the equation given to determine either the sum or product of the roots.2.) Write an equation to find the second root.

Ex) If first root = 5 and sum = 8, then 5 + x = 8Method 2:1.) Plug the first root into the equation for x to solve for the missing variable.2.) Solve the equation using one of your three methods (factoring, completing the square, or the quadratic formula) to find the second root.Directions: One of the roots is given. Find the other root.3.) The equation has one root equal to –3. Find the other root.

4.) The equation has one root equal to 4. Find the other root.

Practice Problems 5.) The equation has one root equal to 5. Find the other root.

6.) The equation has one root equal to -3. Find the other root.

Day 9 – Given One Root, Find the Second Root of an EquationHOMEWORK

**Complete any Practice Problems from class work that have not been completed**Directions: One of the roots is given. Find the other root.1.) , one root = –5 2.) The equation has one root

equal to 3. Find the other root.

3.) , one root = -4 4.) , one root = 3

Review

5.) Solve for x:

6.) Simplify:

7.) For what values of x is the fraction undefined?

8.) Find the solution set and graph : 9.) Solve for x:

Day 10 – Solving Higher Degree Polynomial Equations Using Factor by GroupingDo Now: (Questions 1 & 2)1.) If one root of the equation is , what is the other root? (1) (3) 3 (2) (4) 5

2.) If one root of a quadratic equation is 3 and the product of the roots is 15, what is the value of b if the equation is in the form and . (1) 5 (3) 8 (2) -5 (4) -8

Steps for Solving Using Factor by GroupingConsider the expression:

1.) Move all terms to one side on the equation: (Keep the leading coefficient positive)

2.) Examine this example as two sets of binomials: and . (When viewed independently, each binomial contains a different greatest common factor.

3.) Rewrite each binomial expression in factored form: + . (Notice that the two binomials now contain a common factor in the parentheses.

4.) The factor becomes the new GCF and the “leftovers” go in the other set of parentheses.5.) Therefore in factored form = 0.6.) Set each factor equal to zero and solve. (T-OFF)

(Note: When x2 equals a number, you need the positive and negative square root.)Directions: Solve each equation by grouping.

3.) 4.)

5.)

Practice Problems

Directions: Solve each equation by grouping.6.) 7.)

Day 10 – Solving Higher Degree Polynomial Equations Using Factor by Grouping

HOMEWORK**Complete any Practice Problems from class work that have not been completed**Directions: Solve each equation by grouping.1.) 2.)

3.) 4.)

Review

5.) Express in simplest form: . 6.) Find the solution set:

7.) Express in simplest form:

8.) Find the product of in simplest radical form.

Day 11 – Solving Higher Degree Polynomial Equations

Do Now: (Questions 1 & 2)1.) Factor the following: (1) (3) (2) (4) not factorable

2.) Factor the following: (1) (3) (2) (4)

Steps for Solving Higher Degree Equations1.) Use all of your factoring skills: GCF, DOTS, Trinomials, and Grouping. 2.) Set each factor equal to zero. (T-OFF)3.) Solve

Directions: Use your factoring skills to find all solutions for x. 3.) 4.)

5.) 6.)

Practice Problems Directions: Use your factoring skills to find all solutions for x. 6.) 7.)

Day 11 – Solving Higher Degree Polynomial EquationsHOMEWORK

**Complete any Practice Problems from class work that have not been completed**

Directions: Solve each equation.1.) 2.)

3.) 4.)

Review

5.) Write in simplest form: 6.) Find the solution set of the equation x2 – 2x – 8 < 0 and graph on a number line.

7.) For what value(s) of x does ?8.) Solve by completing the square.


Do Now: (Questions 1 & 2)1.) What are the solutions of this equation ? (1) {-1 , 1} (3) {3, -3, 1} (2) {-1, 1, 3} (4) {-1, 1, -3, 3}

2.) What are the solutions of this equation: ?

(1) (3)

(2) (4)

Steps for Solving Higher Degree Equations by Graphing1.) Move all terms to the same side of the equation.2.) Enter the equation into y = on your calculator.3.) Graph the equation.4.) To identify the real roots use the calculator’s 2nd TRACE function.5.) Choose option number 2. (zero)6.) You must identify the left bound of the zero, so move your cursor to the left of the first zero and

press ENTER.7.) Move your cursor to the right of the zero you wish to identify. Then press ENTER.8.) To guess, press ENTER again and you will see the solution. (x = ?)9.) Repeat the steps for all zeros.

Directions: Solve each equation using your graphing calculator.

3.) 4.)

5.) 6.)

Practice Problems Directions: Solve each equation using your graphing calculator.7.) 8.)


HOMEWORK**Complete any Practice Problems from class work that have not been completed**Directions: Solve each equation using your graphing calculator.1.) 2.)

3.)

Review4.) Find the roots by completing the square:

5.) Find the roots by using the quadratic formula, in simplest radical form:

6.) Find the three binomial factors of by factoring.

7.) Write the quadratic equation given the roots -3 and 5.

Day 13 – Solving Systems of Equations Algebraically

Do Now: (Questions 1 & 2)1.) The zero(s) of the following graph are

(1) x = 0(2) x = 0 and x = 2(3) y = 0(4) y = 0 and y = 2

2.) Find the zeros of

Steps for Solving Systems of Equations AlgebraicallyMethod 1

1. Solve each equation for y in terms of x.2. Set the equations equal to each other.3. Solve for x.4. Plug the value(s) of x into one of the equations and solve for y.

Method 21. Solve one equation for y2. Replace the y with its equivalent in the second equation.3. Solve for x.4. Plug the value(s) of x into each equation and solve for y.

Directions: Solve each of the following system of equations algebraically.

3.) 4.)

Practice Problems Directions: Solve each of the following system of equations algebraically.

5.) 6 .)

Day 13 – Solving Systems of Equations AlgebraicallyHOMEWORK

**Complete any Practice Problems from class work that have not been completed**

Directions: Solve each of the following system of equations algebraically.

1.) 2.)

3.)

Review4.) Find the solution set of . 5.) Express in simplest radical form the sum of

6.) Factor completely:

7.) Simplify:

Day 14 – Solving Systems of Equations / Inequalities GraphicallyDo Now: (Questions 1)

1.) Solve the following system of equations algebraically:

Steps to Solving Quadratic Inequalities in Two Variables 1.) Solve for y in terms of x. (Solve for y)2.) Graph the quadratic function. (Solid line for equal and dotted line for strictly greater than or less

than.)3.) Shade the appropriate region by using a test point (or your calculator).

Directions: Graph the given inequality, and label the solution set with S.2.)

3.)

4.) Solve the system by graphing and determine the common solution point(s).

Practice ProblemsDirections: Graph the given inequality, and label the solution set with S.5.)

Day 14 – Solving Systems of Equations / Inequalities GraphicallyHOMEWORK

**Complete any Practice Problems from class work that have not been completed**Directions: Graph the given inequality, and label the solution set with S.1.)

2.)

3.) Solve the system by graphing and determine the common solution point(s).

Review

4.) Rationalize the denominator:5.) Express in simplest form:

6.) Find the roots by completing the square:

7.) Solve for all values of x:

Day 15 – Review1.) Solve for all roots by completing the square:

2.) Solve for all roots using the quadratic formula in simplest radical form:

3.) Without solving the equation, find the sum and product of the roots:

4.) Write a quadratic equation with integer coefficients when one root is .

5.) Find all the zeros of the given equation:

6.) Find the common solution algebraically, in simplest radical form.

7.) a.) Graph b.) Is the point (0, 0) a solution to the inequality?

8.) If and one root is 2, find the other root and the value of k.

9.) Find the solution set and graph the solution on a number line:

10.) Solve for all values of x:

11.) Solve: 12.) Solve:

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