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
 * vertex
 * x-intercept
 * y-intercept
 * increasing
 * decreasing
 * maximum
 * minimum
 * parabola

1. Quadratic- equation that has more terms when one varible is rasied to the power of two. 2. Vertex- 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 bigger 6. Decreasing- Making something smaller 7. Maximum- The largest value. 8. Minimum- The smallest value. 9. Parabola- A curve shaped on a 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.

__ **Similarities** __


 * They are graphs.


 * __Differences__ **


 * quadratic= y= ax^2+bx+ linear= y=mx+b
 * quadratic parabola. linear= straight line
 * quadratic= must be squared term.. linear= variables first power.

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? The graphical shape the football created was a parabola.
 * Identify the vertex. 23
 * 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 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?


 * graphs are parabolas.
 * have different y intercepts.
 * Function 2 and 3 are the only graphs that have an x intercept.
 * Function 1 and 3 graphs are going up when function 2 is facing down.

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) equation to zero
 * 2) factor
 * 3) factor to find the solutions.
 * 4) Solutions are x-int we solved for x when y=0.
 * Joey isn't wrong