In at least 250 words, please respond to the following:

• Compare quadratic functions with linear functions. Give at least one similarity and one difference.
• Do a little research and use your creativity to come up with a real-life situation that involves a quadratic relationship that hopefully is relevant to the grade level you teach. Your real-life situation MUST be modeled using a quadratic function.

Peer response 1

donna

Quadratic functions and linear functions have some similarities. Both the quadratic and linear function can be graphed. A T-chart can be utilized to help with graphing both the quadratic and linear function. Both the quadratic and linear function have a y-intercept.

The quadratic and linear functions have some differences. The linear function is a line and a quadratic function is curved. To graph a linear function, you need two points and to graph a quadratic function, you need three points. A linear function has a constant change in both the x and y values. A quadratic function has a constant change in the x- value but not the y-value. You can determine that the function is quadratic by finding the change in the change of the y-value. If the change of the change of the y-value is constant then the function is quadratic. The linear function has a constant slope but the quadratic function does not.

A real world situation of a quadratic relationship is driving a golf ball. Elementary students can relate to golf and we could use a children’s golf set to demonstrate the curve of the driven golf ball. We could measure the height of the ball at various times between when it is hit and when it lands. It starts at zero when it is hit and goes up to its highest point and then begins its descent back to the ground. The x-value (independent variable) would be the time and the dependent variable (y-value) would be the height of the ball.

Peer response 2

There are a few differences and similarities between quadratic and linear functions. One difference in these equations is that the graph of a linear function is a straight line while a graph of a quadratic function is a curved line. They can also be similar. These two functions both have a slope. However, the slope of a linear function is constant while the change in the slope of a quadratic function remains constant.

A boy throws a ball into the air from the top of a barn. Its height (h) above the ground in yards after t seconds is given by the function h(t)=−5t^2+10t+20

1. What was the maximum height of the ball that was thrown?
2. How long was the ball in the air before it came back down to the ground?
3. At what time(s) will the ball be at a height of 10 yds?

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