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Question

Identify some distinct characteristics of the graph of a quadratic function.

Make use of the coefficients a, b, & c of the function to answer the following questions:

1) How can one tell if the graph is symmetric?

2) How can one tell whether the graph opens up or down? 3) How can you determine the axis of symmetry of the graph from the coefficients?

4) How would one know if the graph has a maximum value or a minimum value?

5) How do you determine the coordinates of vertex of the graph?

Answer 1

1.  Assuming you mean symmetric around the x-axis, the graph of a quadratic is symmetric when b = 0.  All quadratics are symmetric around their axis of symmetry.

2.  The sign on a will determine if the graph opens up or down.  If the sign is positive, the graph opens up.  If the sign is negative, the graph opens down.

3.  The axis of symmetry can be determined by dividing the opposite of b by 2a.  The equation for the axis of symmetry is x =-b/(2a).

4.  If the a value is positive, there will be a minimum.  If the a value is negative, there will be a maximum.

5.  To find the coordinates of the vertex, first find the equation of the axis of symmetry (see #3).  Using this value for x, substitute into the original equation to find y.  This is the coordinate of the axis of the vertex.