Unit+5+Journal

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. 1. Quadratic- An equation that has more terms when one varible is rasied to the power of two. 2. Vertex- A point where two or more straight lines meet. 3. X-intercept- A point on the graph that intersects with the x-axis. 4. Y-intercept- A point on the graph that interscets with the y-axis. 5. Increasing- Making someting big either in size or quantity. 6. Decreasing- Making something smalller either in size or quantity. 7. Maximum- The largest value. 8. Minimum- The smallest value. 9. Parabola- A curve shaped like an arch.
 * __ 5.1 __**
 * quadratic
 * vertex
 * x-intercept
 * y-intercept
 * increasing
 * decreasing
 * maximum
 * minimum
 * parabola

__** 5.2 **__ Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function. A linear function is a function that has no exponents has one variable and when graphed a line is shown .A linear equation can be written as f(x)=mx+b. A quadratic function is a function that is polynomial and it can also be referred to as the 2nd degree polynomial this is because the highest exponent is 2 and when you graph this you get a "U" shape which is called a parabola.

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
 * __ 5.3 __**

Answer the following questions in your wikispace.
 * 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.

Answers:
 * "U" shaped
 * Vertex is (71,32)
 * X-coordinate represents the time in seconds that the football is thrown in the air.
 * Y- coordinate represents the total feet that the ball is thrown
 * The highest point of the ball was at 71 feet

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

[|5.4.doc]

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?



All three graphs are parabolas however they arent all the same. The y-intercepts are all different and so are the x-intercepts. Two out the three graphs have the same direction they are positive. The slope determines the direction of the graph. The X2 is what makes the graph a parabola.


 * __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.
 * 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?

Answers:
 * The shape is a decreasing "U" parabola
 * h(1)=27 The one means one second
 * The y-intercept is 3 and means how high the tennis ball went
 * Vertex is (1.25,18) The vertex represents the line of symmetry
 * The x-intercepts are -.07 and 2.57 they represent the seconds.

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.
 * __ 5.6 __**

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?

The zero property rule states that the product of two nonzero elements is nonzero. ab=0 then either a=0 or b=0 Joey put one of his solutions as 3 instead of -1.5 and also he subtracted 3 on both sides and left x alone instead of dividing it by 2.

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).
 * __ 5.7 __**

[|5.7.doc]

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?
 * What type of equation was the hardest to match?
 * How did you narrow down your choices?



Answers:
 * I match the negative and positive with the graphs that match
 * The hardest to match was standard form
 * I narrowed down by using the negative and positive and the vertexes