Unit+5+journal

5.1: Quadratic- involving the second and no higher power of an unknown quantity or variable: "a quadratic equation". Vertex- The highest point; the top or apex. X-intercept- The x-coordinate of the point where a line intersects the x-axis. Y-intercept- If the graph of an equation intersects the y-axis at the point (0,b) the number b is the y-intercept of the graph. Increasing - When the graph starts to increase. Decreasing-When the graph starts to decrease. Maximum- Graph cant go any higher. Minimum- Graph cant go any lower. Parabola-The set of all points equidistant from a point called the focus and a line called the directrix.

5.2: Summarize the similarities and differences between linear functions and quadratic functions. Discuss the graphs, the equations and the properties of each function. //**The linear function is y=mx+b, the quadratic function is ax squared +bx +c. Its almost the same because of the variables. When you graph a quadratic function it will be a "U" shape, when you graph a linear function it would be a straight line. In order to solve a quadratic function you have to plug it into the quadratic formula. In order to solve a linear function you have to plug 0 for y and 0 for x.**//

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? //**upside down U shape.**//
 * Identify the vertex. //**(75,22)**//
 * Describe, in context, what the x-coordinate of the vertex represents. //**Is the distance down the field.**//
 * Describe, in context, what the y-coordinate of the vertex represents. //**Is the highest point.**//
 * Find f(2). Describe what your answer means in the context of the problem. //**f(2)= -10636. 2 feet down the field and -10636ft in the "air"**//

5.4: In your wiki space 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? //**They are all similar because they share a common U shape. Function 2 is different from function 1 and 3 because it opens down instead of up. When the first number or variable is a negative it opens down, and if it is a positive than it opens up. Function 1 and 3 x-values are both negative and y-values end up being positive. Function 2 x-values are positive and y-values end up being negative.**//

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. //**Upside down U shape.**//
 * Find h(1). Describe what h(1) means in the context of the problem. //**h(1)=27 In 1 second the ball is 27ft in the air.**//
 * What is the y-intercept of h(t). In context, what does the y-intercept represent? //**y-intercept is 3 which means the guy serves the ball once its 3ft up in 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. (1.25,28) at 1.25 sec the ball reached its highest height of 28.**//
 * What is the x-intercept(s) of h(t). In context what does the x-intercept(s) represent? //**0.078 and 2.42 they represents where the ball starts and where it ends.**//

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: 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? //**I separated them into 3 different groups of vertex forms intercept form and standard form and did vertex form first.**//
 * What type of equation was the hardest to match? //**Standard form because you have to factor them to get the x-intercepts.**//
 * How did you narrow down your choices? //**By figuring out the vertex,y-intercept,and x-intercept for each graph the divided the equations into 3 groups of vertex form,intercept form and standard form.**//