Unit+3+-+Sovling+Quadratic+Relations

3.11 Solving Quadratic Relations
Case 1: Solving quadratic equations with no linear term. Method: isolate the quadratic term and solve.

Case 2: Solving quadratic equations with a linear term. Method: rearrange the equation so one side equals 0. factor and solve.

Note that "finding the **roots** " means finding the zeros

HW: p. 315 # 2agik, 3, 6de, 13, 17

3.12 Sample Problems.
A fifth problem type is where you are given an object like a bridge. You can create two zeros by placing a sketch on the x-axis, and you are given another point. From this you can find the equation that models the bridge and find the vertex.

A sixth type of problem uses the Pythagorean theorem.


 * UNIT TEST Wednesday April 28th,**
 * Vocabulary** - roots, zeroes, parabola, quadratic, monic, complex, perfect square, difference of squares.

- second differences, know how to calculate and whether the graph opens up or down.

- Given Factored Form
 * find zeros
 * find equation of axis of symmetry
 * find vertex
 * draw an reasonably accurate graph
 * use FOIL to expand into standard form
 * find y-intercept (by expanding and using c as y-intercept)
 * find 'a' and know how it affects the direction of opening

Given a graph
 * finding the roots, vertex and axis of symmetry from a graph of a parabola

Given standard form
 * convert to factored form by factoring.

Solving quadratic relations to problem solve. See the five types of problems in


 * Skills needed**
 * finding zeros (roots)
 * finding midpoint
 * expanding
 * factoring (common, monic and complex)