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Chapter 4 - Qudratic Relations

Ontario Curriculum

Overall Expectations:

• determine the basic properties of quadratic relations;

• relate transformations of the graph of y = x2 to the algebraic representation y = a(x – h)2 + k;

• solve problems involving quadratic relations.

Specific Expectations:

- determine, through investigation with and without the use of technology, that a quadratic relation of the form y = ax2 + bx + c (a ≠ 0) can be graphically represented as a parabola, and that the table of values yields a constant second difference

- 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)

- compare, through investigation using technology, the features of the graph of y = x2 and the graph of y = 2x, and determine the meaning of a negative exponent and of zero as an exponent

- identify, through investigation using technology, the effect on the graph of y = x2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k

- explain the roles of a, h, and k in y = a(x – h )2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry;

- sketch, by hand, the graph of y = a(x – h )2 + k by applying Transformations to the graph of y = x2

- determine the equation, in the form y = a(x – h)2 + k, of a given graph of a parabola.

- 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);

- determine the zeros and the maximum or minimum value of a quadratic relation from its graph (i.e., using graphing calculators or graphing software) or from its defining equation

- 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