1a. All of the graphs have been parabolas and the tables increased in a pattern and decreased in the same pattern after the middle point.
b. With both, it increases in the same pattern and then decreases in that pattern when it reaches the middle point.
2. You can multiply the x-value of the middle point by 4 or double the number in the equation.
3. For tables of quadratic functions, the y-value increases until it reaches the middle point, then decreases in the same pattern. For tables of linear functions, both values increase at a steady rate. For tables of exponential functions, the y-value doesn't increase at a steady rate or with a pattern. The graphs of quadratic functions are parabolas and the middle point is called the vertex. The graphs of linear functions are straight lines. The graphs of exponential functions start at a slow increase and then increase rapidly. The equations all have different parts that make them that certain kind of equation. In a quadratic function, the equation has a variable multiplied by a quantity. A=l(1/2P-l). In a linear function, the equation multiplies two variables and adds another. y=mx+b. In an exponential function, the equation raises a variable to a certain power and multiplies another number to it. y=ab^x.
Emily L. and Alex S.
Friday, April 30, 2010
Thursday, April 29, 2010
Math Reflection...to be corrected if wrong!
Lately in Algebra 1, we have been observing the graphs and tables of quadratic functions. The examples we have been using revolve around the relationship between rectangles lengths and areas.
1.a) In the tables we have been viewing, as the length increases, the area increases. This continues until the table reaches the half-way point within the set of length values. At this point the area is the greatest it has been in the table, and then begins to decrease in the opposite way that it increased. The graphs we have observed have all been parabolas that open down. The arch shaped lines The line increases at a curve, and then comes to a summit where the area is the largest, and then decreases at a curve symmetrical to the increasing curve.
1.b)The patterns in a quadratic functions graph also appear in a table. They both increase with the length until the graph/table reaches a maximum area and they decrease in the opposite order that the numbers increased.
2.)One way to find the maximum area of a rectangle with a fixed perimeter is to make a graph or table. The highest point on the graph is the largest area and the x-axis value below that point would be the length that corresponds with the area. Another way to find the maximum area is to square the length of the rectangle. A rectangles length squared is always the maximum area.
3.) The graphs, tables and equations of quadratic functions are different from those of linear and exponential functions. The graph of a quadratic functions are different from linear graphs because they are not straight lines. They are not like exponential functions because they both increase and decrease in one graph. They increase and decrease with a pattern, and end up looking like an arch not a line or a increasing or decreasing curved line. The table of e quadratic function is different from one of a linear function. Unlike a table of e linear function, a table of a quadratic function doesn't increase of decrease at a fixed rate. A table of a quadratic function doesn't multiply of divide itself like one of an exponential function does. The equation of a quadratic function is not like one of a linear function be. this is because it includes exponents which a linear function doesn't. ( for example like finding the width using an equation like 30l-l^2) It isn't like one exponential because in an exponential function the variable is the exponent. But, in a quadratic function the variable is the number that the length is being subtracted by. ( 1/2 of the perimeter). Instead of the exponent changing from equation to equation, in a quadratic function the fixed perimeter of the rectangle is the variable....I think. :-)
by Kate M. and Allie G.
1.a) In the tables we have been viewing, as the length increases, the area increases. This continues until the table reaches the half-way point within the set of length values. At this point the area is the greatest it has been in the table, and then begins to decrease in the opposite way that it increased. The graphs we have observed have all been parabolas that open down. The arch shaped lines The line increases at a curve, and then comes to a summit where the area is the largest, and then decreases at a curve symmetrical to the increasing curve.
1.b)The patterns in a quadratic functions graph also appear in a table. They both increase with the length until the graph/table reaches a maximum area and they decrease in the opposite order that the numbers increased.
2.)One way to find the maximum area of a rectangle with a fixed perimeter is to make a graph or table. The highest point on the graph is the largest area and the x-axis value below that point would be the length that corresponds with the area. Another way to find the maximum area is to square the length of the rectangle. A rectangles length squared is always the maximum area.
3.) The graphs, tables and equations of quadratic functions are different from those of linear and exponential functions. The graph of a quadratic functions are different from linear graphs because they are not straight lines. They are not like exponential functions because they both increase and decrease in one graph. They increase and decrease with a pattern, and end up looking like an arch not a line or a increasing or decreasing curved line. The table of e quadratic function is different from one of a linear function. Unlike a table of e linear function, a table of a quadratic function doesn't increase of decrease at a fixed rate. A table of a quadratic function doesn't multiply of divide itself like one of an exponential function does. The equation of a quadratic function is not like one of a linear function be. this is because it includes exponents which a linear function doesn't. ( for example like finding the width using an equation like 30l-l^2) It isn't like one exponential because in an exponential function the variable is the exponent. But, in a quadratic function the variable is the number that the length is being subtracted by. ( 1/2 of the perimeter). Instead of the exponent changing from equation to equation, in a quadratic function the fixed perimeter of the rectangle is the variable....I think. :-)
by Kate M. and Allie G.
Wednesday, April 14, 2010
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Getting a comment can be like receiving a little bouquet in your mailbox: a treat for the senses.
Guidelines
• Make your comment worth reading.
• Start a conversation.
• Be positive, interested, and encouraging.
• If you disagree, be polite about it.
• Connect with the post: be on topic.
• Re-read your comment before you hit submit–think before you send!
• Aim for correct spelling, punctuation, and grammar.
• Don’t use chat or texting language like lol, i, or u.
• No “Hi! Nice Job! Bye!” comments. Be thoughtful.
• Keep your privacy: no personal or identifying information about you, your family, or your friends. Don’t give out last names, school name, phone numbers, user names, or places and dates you can be found.
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