Warm up: In order to pay for upkeep of a local highway, the transportation department has set up tollbooths at each of the highway’s exits. Drivers are charged a toll of $1.20 for use of the highway, and are then charged an additional $0.04 per mile driven. 1. Write an algebraic expression that can be used to represent the total toll charged if m represents the number of miles driven.  2. What is the toll charged to drive 14 miles on this highway?

Interpreting Structure in Expressions Lesson 5.1 Interpreting Structure in Expressions

# of Terms Name by # of Terms Monomial 2 Binomial 3 Trinomial 4+ Polynomial

Degree Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic (largest exponent) Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic

A quadratic expression can be written in the form ax2 + bx + c, where x is the variable, and a, b, and c are constants. Both b and c can be any number, but a cannot be equal to 0 because quadratic expressions must contain a squared term.

Example 1 Identify each term, coefficient, and constant of 6(x – 1) – x(3 – 2x) + 12. Classify the expression as a monomial, binomial, or trinomial. Determine whether it is a quadratic expression.

Example 2 Translate the verbal expression “take triple the difference of 12 and the square of x, then increase the result by the sum of 3 and x” into an algebraic expression. Identify the terms, coefficients, and constants of the given expression. Is the expression quadratic?

Example 3 A fence surrounds a park in the shape of a pentagon. The side lengths of the park in feet are given by the expressions , 3x + 1, 3x + 2, 4x, and 5x – 3. Find an expression for the perimeter of the park. Identify the terms, coefficients, and constant in your expression. Is the expression quadratic?

Example 4: Deck the Deck Shanna wants to decorate the triangular deck behind her house. The base of the triangle is 10 meters shorter than the altitude. What are the terms, factors, and coefficients of the quadratic expression that represents the area of the deck to be decorated?

Example 5 Show that (x + 2)(2x – 1) is a quadratic expression by writing it in the form . Identify a, b, and c.

Example 6. What values of x make the expression (x + 2)(x – 3) positive?

Example 7. The length of each side of a square is increased by 2 centimeters. How does the perimeter change? How does the area change?