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.
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5 comments:
I like how much detail you put in this. I also think the detail put is very accurate and had similar answers.
Very well written. You put a lot of detail in and clarified a lot for me. I also liked your humor!
Hi Kate and Allie,
I really liked the way you explained this. It helped me better understand quadratic functions. Also, number 3 really helped me understand the differences between quadratic, linear and exponential functions. I wasn't quite sure about that before but now I get it. :)
This is really good! It helped me understand things a lot better. I liked all your hard work and detail. It is very specific and easy to understand.
Hi!!! I thought that your explanation was very clear, and really helpful. I was confused especially on the equations of quadratic functions, and your explanation really cleared it up for me. Great job!!!
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