## HSII.1 Quadratic Functions (A3)

Students examine and model contexts which change quadratically and compare these to familiar linear and exponental contexts.

Students examine and model contexts which change quadratically and compare these to familiar linear and exponental contexts.

Students use their knowledge of quadratic functions to model and solve problems. Studnets understand solving quadratics as a process of reasoning and use algebraic properties and rules to form equivalent expressions and equations, which allows them to convert between standard, vertex, and factored form by factoring, completing the equare, and distributing. Students also derive and make use of the quadratic formula.

Students extend their understanding of irrational numbers, expand their knowledge of exponents to include any rational number, and expand their knowledge fo the number system to include imaginary and complex numbers and explore how these numbers behave under famiilar operations.

Students describe dilations in terms of center and scale factor and use these terms to describe properties of dilations. They then prove and use theorems about triangles, prove and use slope criteria for parallel and perpendicular lines, and construct points that partition a line segment into a given ratio, and explore why circles are similar.

Students examine side ratios of similar triangles, develop an understanding of sine and cosine and use the relationship betweeen these two ratios to solve problems.

Students develop more sophisticated although still informal, arguments for the circumference, area, and volume formulas they learned in earlier grades and then use these formulas to model and solve a variety of problems.

Students begin considering compound events as subsets of sample spaces. Students examine situations involving pairs of independent and non-independent events, and they calculate probabilities of compound events in unifrom probability models.