Looking for patterns in linear sequences and quadratic sequences Solving and manipulating quadratic equations The characteristics of the graph of a quadratic function Creating quadratic models using technology in order to solve real life problems to do with projectile motion
Conceptual Framework
relationships equivalence in the context of Identities and relationships
Statements of Inquiry
Decision-making can be improved by using a model to represent relationships
Factual
How can we use quadratic functions to model projectile motion?
Conceptual
How does the determinant tell us the number of solutions to a quadratic equation?
Debatable
How accurate do quadratic models need to be?
Description
This unit will explore situations in which an object is thrown. The relationship between vertical and horizontal displacement is parabolic. This relationship can be expressed as a quadratic function. By the end of the Unit the students will be able to use technology to model projectile motion and use these models to answer questions related to the real life situation. The idea of equivalence will be explored in the context of the relationship between algebraic expressions and their graphical representations. However, before exploring parabolas the students will review how to solve quadratics equations and how to plot parabolas using the TI-84 Plus. The modelling of projectile motion is a great example of converting a real life situation into an algebraic expression.
Learning Outcomes
Review linear sequences
Introduce the formula for finding any term in a sequence knowing the first term and the difference between consecutive terms
Introduce the formula for the sum of terms in a sequence, known as a series
Review expansion of binomial expressions leading to factorising quadratics
Solve quadratic equations by factorising, completing the square, using the quadratic formula and using technology
Explore the shape of a quadratic and basic features using technology
Apply the above knowledge to model projectile motion e.g. Dan Meyer’s “Will it hit the hoop?” task