<p>Unit 5- Interpret the structure of expression Notes #1 </p><p>1. Given the expression 6(x- 1) - x (3 - 2 x ) + 12 complete the following:</p><p> a) Simplify the expression ( Hint: Distribute, and combine like terms)</p><p> b) How many terms are in the expression?</p><p> c) Identify all the coefficients in the expression</p><p>-The coefficient of X2 is ____</p><p>-The coefficient of X is ____ </p><p> d) What is the constant in the expression? ______</p><p> e) Classify the expression as a monomial, binomial or trinomial.</p><p> 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</p><p>Is the expression from e above a quadratic expression? _____</p><p>Explain. Unit 5- Interpret the structure of expression Notes #1 </p><p>Example1: Translate the verbal expression below into an algebraic expression. Identify the terms, coefficients and constants of the given expression. Is the expression quadratic?</p><p>“Take triple the difference of 12 and the square of x, then increase the result by the sum of 3 and x “.</p><p>Step 1: Break down the expression into parts using the given information</p><p>Step 2: Simplify the expression by distributing and combining like terms. Unit 5- Interpret the structure of expression Notes #1 </p><p>Step 3: Identify the terms, Coefficients and Constants.</p><p>Terms: </p><p>Coefficients:</p><p>Constant:</p><p>Quadratic? Yes or No</p><p>Practice 1: Write the given verbal expression as an algebraic expression. Identify the terms, constants and coefficients and determine if the expression is Quadratic.</p><p>“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 </p><p>Example 2: What values of x makes the expression (x + 2) (x – 3) positive?</p><p>Process: The expression will be positive if both factors are positive or both factors are negative.</p><p>What X values will make (x+2) positive? ______</p><p>What X values will make ( x-3) positive? ______</p><p>What X values will make ( X+2) negative? _____</p><p>What X values will make (X-3) negative? ______The value of the expression (x + 2) (x – 3) is positive when ____ is ______or ____ is ______.</p><p>Practice 2: What values of x make the expression (x + 7)(x – 10) negative?</p><p>Problem Solving: Answer the following problems with your partners/groups.</p><p>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).</p><p>3x (2x + 8) + (x – 3) (x + 10) Unit 5- Interpret the structure of expression Notes #1 </p><p>2. Translate any verbal expressions to quadratic expressions, and then answer the questions.</p><p>“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?”</p><p>(Hint: Write the expression for the original surface area, and then write the expression for the new surface area and compare)</p><p>3. What values of x make the expression (x + 2) (x – 5) negative?</p>