By the end of this lesson you will be able to:

- describe the shape of a parabola, the axis of symmetry, and the vertex

- Use finite differences to determine if a function is linear or quadratic

- graph a parabola using a table of values

Ontario Curriculum

Overall Expectations:

• determine the basic properties of quadratic relations;

• 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)

- 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