Chapter 6 - Quadratic Equations

 

Ontario curriculum


Overall Expectations

- solve quadratic equations and interpret the solutions with respect to the corresponding relations;

- solve problems involving quadratic relations.

Specific Expectations:

- identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value), and use the appropriate terminology to describe them;

- factor polynomial expressions involving common factors, trinomials, and differences of squares

- determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts (i.e., the zeros) of the graph of the corresponding quadratic relation, expressed in the form y = a(x – r)(x – s)

- interpret real and non-real roots of quadratic equations, through investigation using graphing technology, and relate the roots to the x-intercepts of the corresponding relations;

- express y = ax2 + bx + c in the form y = a(x – h)2 + k by completing the square in situations involving no fractions, using a variety of tools

- sketch the graph of a quadratic relation that is given in standard form

- explore the algebraic development of the quadratic formula - solve quadratic equations that have real roots, using a variety of methods

- determine the zeros and the maximum or minimum value of a quadratic relation from its graph

- solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology