8/31/15 Alg 2

Bellwork 8/31/15

Determine the value for c that would create a perfect square trinomial.1.

State the transformations:2.

Evaluate for the given value:

3.

4. What is the domain for ?

X F(x)

0

1

2

3

4

How do I know what x-values to use?• You need at least 5 x-

values.• The “middle” x-value

should be the x-value of the vertex.

Vertex is either the maximum or minimum point on the graph of a quadratic.

For:

The vertex is

If a is +, then the vertex is a minimum, and the parabola opens up.If a is -, then the vertex is a maximum, and the parabola opens down.

X F(x)Vertex-2Vertex-1Vertex vertex

Vertex+1Vertex+2

Bellwork 9/1/15

Determine the value for c that would create a perfect square trinomial.1.

Evaluate for the given value:

3.

4. What is the domain for ?

Find the vertex for the given functions

𝑓 (𝑥 )=𝑥2−6 𝑥+2

Decide if the vertex is a max or a min, and which way the parabola opens. What is the domain and range of each?

𝑓 (𝑥 )=𝑥2−6 𝑥+2

Your turn: find the vertex, and state max or min, and how the parabola opens.

Axis of symmetry—an imaginary line that divides the parabola down the middle. It always goes through the vertex, so is the equation for it.

Forms of quadratic functions

General Form of a Quadratic: Standard form of a Quadratic:

Bellwork 9/2

Find the vertex for the following and state whether it represents a maximum or minimum value.

3. Write the domain and range for the functions in #1 and #2 using interval notation.

Solving quadratics by graphing.

The solutions to a quadratic have a few different names1. Roots2. Zeros3. Solutions4. X-intercepts

Find the solutions if they exist, describe the domain and range in interval notation.

Understanding the Vertex

1. If the vertex is (-1, -3) and the parabola opens down, how do we know that there are no real zeros?

2. If the vertex is (9, 0) how do we know that there is one real zero?

3. Vertex is ______ and the parabola opens down and has 2 real zeros.

4. Vertex is (-1, -3) and the parabola opens up. The quadratic has __ solutions.

What are the solutions? Describe the domain and range.

Bellwork 9/2

Find the vertex for the following and state whether it represents a maximum or minimum value.

3. Write the domain and range for the functions in #1 and #2 using interval notation.

Use quadratic equations to solve

1. Find two real numbers whose sum is -17, and their product is 72.

Bell work 9/3/14

Find the vertex and complete the table and graph the quadratic.

X F(x)

Factoring review. Factor to solve.

1. 2.

You try. Solve by factoring.

Algebra 2You will be tested on your memory of the perfect squares from to , and on your memory of the perfect cubes from to . Copy down the table, extend it to cover what you need to know, and start practicing. There will be 3 quizzes, and they will not be announced ahead of time.

1 1 12 4 83 9 274 16 645 25 1256 36 2167 49 3438 64 5129 81 729

10 100 100011 121

Bellwork 9/3/15

Find the vertex.

1. State the domain and range for #1.

Solve by factoring, if possible.

Solving quadratic equations with the square root propertyExample 1: You try:

Example 2: You try:

Bellwork 9/4/15 (do not waste time writing the problem down)A baseball is hit with an initial velocity of 36 feet per second from a height of 2 feet. The height of the ball after being hit can be modelled by the equation: . Where h(t) is the height of the ball, and t is time in seconds. What is the height of the baseball 1.4 seconds after it is hit?

Perfect square test

• No calculators• Do not show any work • Write your name on the paper now• You must write the problem to get credit• Example:

• You will have 60 seconds

Write the Problems!!!1. 2.

3. 4.

𝑦=2 𝑥2−4 𝑥−16 Converting to standard form

Solving quadratics by completing the squareExample 1: Steps for completing the square:

1. Put ()’s around the terms with x’s.2. Factor out a.3. Make room inside the ()’s 4. Take ½ of the b term and square it

for the CTS term.5. a times the new CTS term and

change the sign for the rebalance number.

6. Factor the trinomial inside the ()’s

Solving quadratics by completing the square

You Try: Steps for completing the square:1. Put ()’s around the terms with

x’s.2. Factor out a.3. Make room inside the ()’s 4. Take ½ of the b term and square

it for the CTS term.5. a times the new CTS term and

change the sign for the rebalance number.

6. Factor the trinomial inside the ()’s

Fill in the blanks for CTS, and then solve.1. 2.

CW # 9 Blue text book

Page 304 (14-31)

Bellwork 9/19

Solve the system Determine the maximum and minimum values for the given objective function using the vertices provided.

a. b. c. d.

Fill in the blanks for CTS, and then solve.1. 2.

Complex Number

All numbers are within the set of complex numbers.2, 5.1, even .

The standard form of a complex number is

Where is the real part, and is the imaginary part.

2 can be written as

5.1 can be written as

The Imaginary Unit

Consider There are no real solutions.

This is the imaginary unit.

is a complex number where 5 is the real part and 3i is the imaginary part.

Numbers with no real part, like are called pure imaginary numbers.

Complex Conjugates

If we have , its conjugate is .

What is the conjugate of ?

Complex conjugates work the same way:The complex conjugate of Is

The product of two complex conjugates is a real number (no i).

We cannot leave i’s in the denominator. So, multiply the top and bottom of the fraction by the conjugate of the denominator to eliminate the imaginary part

Class Work #10 (due 9/22)

#10 Page 311 (CTS)(25, 27, 33, 35, 37, 39)

Honors #10Page 311 (25-47 odd)

Odd answers are in the back of the book. Check your answers before turning in. Must show work for credit.