Unit+5+Journal

‍__** 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-when the x is squared.
 * vertex-the point of a graphed equation.
 * x-intercept-where the line crosses the x axis.
 * y-intercept-where the line crosses the y axis.
 * increasing-when the graph is going up in a positvie way.
 * decreasing-when the graph is going down in a negative way.
 * maximum-the highest amount or point where the line goes to.
 * minimum-the lowest point of the graph.
 * parabola-a U shaped graph.

‍__** 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 functions are lines that may either go up or down. Quadratic functions are things such as parabolas which may open up or down. Linear functions equation is y=mx+b. The equation of the parabola is y=a^2+bx=c.

‍__** 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. A parabola. (75, 22) The highest point that the football reached when Joe threw it. The length that Joe threw the football, like how far it went. The highest point of where the ball reaches.
 * What graphical shape did the football create as it flew through the air?
 * 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.
 * Find f(2). Describe what your answer means in the context of the problem.

‍__** 5.4: **__
Complete the three graphs and tables in the document below. 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?

The graphs are parabolas. The graphs have different y intercepts, as well as the x intercepts. The directions of the graphs are different too. One was positive, the other was negative and again the other one was positive. Because the equations have x^2 it becomes a parabola unlike a linear one which just has x. Slope is important here too because it tells you which way the graph will go either up or down.

‍__** 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.**__ A U shape. Starts from the point where it gets thrown in the air then reaches its highest point and then goes down. h(1)=27, when the ball is in the air for just one second. It represents the height that the tennis ball reached which is three. The vertex can also be viewed as the place where the line of symmetry is found. (0,-.07) & (0,2.57) are the x intercepts. they are the the amount of seconds.
 * What shape does the path of the tennis ball make while traveling in the air.
 * Find h(1). Describe what h(1) means in the context of the problem
 * What is the y-intercept of h(t). In context, what does the y-intercept represent?
 * 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.
 * What is the x-intercept(s) of h(t). In context what does the x-intercept(s) represent?

‍__** 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?

‍__** 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. Usually I would seprate the graphs and equations into two sections. Positive and negative, because it is easier to look at it in that way. Like if the graph goes up you know that it has to be a positive equation, the same goes for the negative ones. I really just sorted them down to whether they opened up or down and went on from there.
 * What properties did you look at first? What types of equation did you match first?
 * What type of equation was the hardest to match?
 * How did you narrow down your choices?