Ideas from Classroom Teachers for
As this is a continuation of year 1, this unit should proceed quickly. This particular portion of the unit allows for alternative types of assessment. Use of a graphing calculator with a statistical package allows for deeper discussion and understanding of this material.
As an introduction to the topic, you can use the following formula as an example of a quadratic function: vt 16t2 = 0, where v represents the initial velocity in feet per second and t the time in seconds for a projectile to hit the ground (i.e. arrow in archery, time in the air; kick of a football, time in the air; fireworks, time in the air).
Use other physics formulas to gather data. Use of probes and meters, if available, to measure time and distance and plot the data. This topic is a good opportunity to have some cross-curricular work or team teaching with the science department.
A good review of factoring needs to be done here. In my opinion, additional factoring methods need to be introduced as well: greatest monomial factor, difference of squares, factoring trinomials, difference of cubes, and sum of cubes.
Concerning graphs of quadratics: Relate the quadratic formula to the x-intercepts, the vertex, and the axis of symmetry.
Complex numbers will be of interest to students in the development of numbers and number theory. Students will need just an introduction to complex numbers since some of the solutions for the quadratics will be written in complex number form. The more in-depth discussion of complex numbers can be done in later courses. B’‘ groups may need to spend more time here, but it is worth it to get them comfortable with complex numbers.
Another opinion on introducing complex numbers: The focus here should be on finding and simplifying roots of negative numbers in the context of solving quadratic equations.
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