Unit+5

= 5.1 =

List the following words and give a mathematical definition in your own words on your wikispace. Remember, you may edit your definitions after we begin the unit.


 * **Quadratic:** An equation containing one or more terms in which the variable is raised to the power of two, but no terms in which it is raised to a higher power.
 * **Vertex:** The highest, or lowest point.
 * **X-intercept:** Where the line passes the x intercept.
 * **Y-intercept:** Where the line passes the y intercept.
 * **Increasing:** Become or make greater in size, amount, intensity, or degree.
 * **Decreasing:** Become smaller or less in size, amount, intensity, or degree.
 * **Maximum:** The greatest or highest amount possible or attained.
 * **Minimum:** The greatest or highest amount possible or attained.
 * **Parabola:** A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.

= 5.2 =

Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function.

**Linear Function:** A function with no exponents other than one, and with no products of the variables (ex. y=x+4, y= -4, and 3x-4y = 1/2 are linear functions) the graph of a linear function is a line. It is a function that has a constant rate of change. It has a graph which is a straight line. The function can be written as f(x) = mx + b, where m and b are real constants and x is a real variable.

**Quadratic function:** A quadratic function, is a polynomial function of the form y=ax^2+bx+c. A quadratic function is also referred to as a degree 2 polynomial or a 2nd degree polynomial, because the highest exponent of x is 2. The graph of this function is a parabola.

= 5.3 =

Joe is standing at the end zone of a football field and throws the football across the field. The function below models the path that football is thrown, in feet. f(x)=-2(x-75)squared +22

__** Answer the following questions in your wikispace. **__


 * **What graphical shape did the football create as it flew through the air?** It displays a parabola.
 * **Identify the vertex.** (71,32)
 * **Describe, in context, what the x-coordinate of the vertex represents.** It displays how long the football was in the air for.
 * **Describe, in context, what the y-coordinate of the vertex represents.** It displays how many yards it flew.
 * **Find f(2). Describe what your answer means in the context of the problem.** The football came in the air and was thrown at a vertex of 71.

= 5.4 =

In your wikispace journal, describe the similarities and differences between the three graphs and equations. Be sure to compare the following features; y-intercept, x-intercepts, direction of the graph. Find the connection between these features and their equations - what causes them?

**Similarities:** All three graphs are parabolas, functions 2 and 3 have the same x-intercepts.

**Differences:** All 3 graphs have different y-intercepts, functions 1 and 3 graphs are going upwards, while function 2 is facing downward.

= **5.5** =


 * You and your friend are playing a game of tennis. Your friend throws the ball in the air, hitting the ball when it is 3 ft above the court with an initial velocity of 40 ft/sec. The height h(t) of the ball can be modeled by **** the function h(t) = -16t^2+40t+3, where t is the elapsed time in seconds after the dive **** . **


 * __ Answer the following questions in your wikispace. __**
 * **What shape does the path of the tennis ball make while traveling in the air?** Its a decreasing line and the tennis ball stays in the air for 3 seconds and then hits the ground.
 * **Find h(1). Describe what h(1) means in the context of the problem?** h(1) = seconds is equal to 1.
 * **What is the y-intercept of h(t). In context, what does the y-intercept represent?** It displays the initial height and when the tennis ball was hit.
 * **Identify the vertex. Describe in context what the x-coordinate of the vertex represents. Describe in context what the y-coordinate of the vertex represents.** Vertex = (1.25,18), x-coordinate is 1.25 and it represents the time in seconds, y-coordinate is 18 and it represents the height after the ball hit, 1.25 seconds.
 * **What is the x-intercept(s) of h(t). In context what does the x-intercept(s) represent?** x = - 40 + the square root of 1792 divided by negative 32.

= 5.6 =

In your own words, explain what the Zero Property Rule is and how and when it is used. Given the equation 0 = (2x-3)(x+5), verbally explain the step-by-step process to solve for x as you would to a brand new student entering our class. You looked over at Joey's paper and noticed he had written 3 and -5 as his two solutions. Explain where Joey may have made his mistake? How would you prove to Joey that his solutions are not true?


 * **Zero Property Rule:** If A x B= 0, then A=0 or B=0.


 * 1) Set the whole equation to 0.
 * 2) Then after you set it to 0, you can use the zero product property to solve each factor.
 * 3) Solve and find the solutions to each of the factors.
 * 4) When you set y equal to 0 we solved for x, then the solutions are x-intercept.
 * 5) Joey's correct only because the solutions are suppose to be switched around after you find them.

= 5.7 =

Listed below are 4 graphs and 12 equations. Some equations are written in intercept form, some in standard form and some in vertex form. A single graph will match one of each type of equation (so 3 equations per graph).

In your wikispace, explain your thought process and order of matching the equations and graphs together.


 * ** What properties did you look at first? What types of equation did you match first? ** Vertex form, standard form, and intercept form.
 * ** What type of equation was the hardest to match? ** Standard form because you have to foil first.
 * ** How did you narrow down your choices? ** I chose the easiest one and then solved.

= WORD DOCUMENTS WOULDN'T UPDATE ON MY COMPUTER......... =