Unit 5- Interpret the structure of expression Notes #1

1. Given the expression 6(x- 1) - x (3 - 2 x ) + 12 complete the following:

a) Simplify the expression ( Hint: Distribute, and combine like terms)

b) How many terms are in the expression?

c) Identify all the coefficients in the expression

-The coefficient of X2 is ____

-The coefficient of X is ____

d) What is the constant in the expression? ______

e) Classify the expression as a monomial, binomial or trinomial.

f) A Quadratic expression is an expression that can be written in the form ax2 + bx + c . The highest exponent in a quadratic equation is 2, and a cannot be = 0

Is the expression from e above a quadratic expression? _____

Explain. Unit 5- Interpret the structure of expression Notes #1

Example1: Translate the verbal expression below into an algebraic expression. Identify the terms, coefficients and constants of the given expression. Is the expression quadratic?

“Take triple the difference of 12 and the square of x, then increase the result by the sum of 3 and x “.

Step 1: Break down the expression into parts using the given information

Step 2: Simplify the expression by distributing and combining like terms. Unit 5- Interpret the structure of expression Notes #1

Step 3: Identify the terms, Coefficients and Constants.

Terms:

Coefficients:

Constant:

Quadratic? Yes or No

Practice 1: Write the given verbal expression as an algebraic expression. Identify the terms, constants and coefficients and determine if the expression is Quadratic.

“The product of 7 and the square of x, increased by the difference of 5 and x2” Unit 5- Interpret the structure of expression Notes #1

Example 2: What values of x makes the expression (x + 2) (x – 3) positive?

Process: The expression will be positive if both factors are positive or both factors are negative.

What X values will make (x+2) positive? ______

What X values will make ( x-3) positive? ______

What X values will make ( X+2) negative? _____

What X values will make (X-3) negative? ______The value of the expression (x + 2) (x – 3) is positive when ____ is ______or ____ is ______.

Practice 2: What values of x make the expression (x + 7)(x – 10) negative?

Problem Solving: Answer the following problems with your partners/groups.

1. Show that the expression below is a quadratic expression by writing it in the form ax2 + bx + c . Identify a, b, and c. (Hint: Distribute and combine like terms).

3x (2x + 8) + (x – 3) (x + 10) Unit 5- Interpret the structure of expression Notes #1

2. Translate any verbal expressions to quadratic expressions, and then answer the questions.

“The surface area of a cube is the product of 6 and the square of the side length. How does the surface area of a cube change when the side of a cube doubles in length?”

(Hint: Write the expression for the original surface area, and then write the expression for the new surface area and compare)

3. What values of x make the expression (x + 2) (x – 5) negative?