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Graphing Quadratic Functions 2 - Finding Points and Drawing the Parabola

Recall:                        
  1. The graph of a quadratic function is called a Parabola.
  2. The Vertex of a parabola is the point at which the parabola stops falling and begins rising (or vise versa).  In other words, it is the point at which the parabola officially “turns the corner”.  {It can also be thought of as the only point on the parabola at which the slope is equal to zero.}
  3. Parabolas are symmetric – both sides are mirror images of each other.
  4. There is an imaginary line down the middle of a parabola called the axis of symmetry. (This line is NOT part of the parabola!)  The axis of symmetry passes through the vertex.
 
HOW TO GRAPH A QUADRATIC FUNCTION:

1)      Locate the vertex (see previous tutorial).

2)      I highly recommend learning a shortcut for graphing other points (see “From the Vertex” and “Point-to-Point” tutorials).

3)      If you have trouble learning and/or remembering a shortcut, you will have to use the function to find more points – I recommend finding three points on each side of the vertex.

·         Use a table of values to organize your points.

·         Write the vertex in the middle of this table.

·         Choose x-coordinates (I recommend three of them) on each side of the vertex and write these in the table.

·         For each x-coordinate, you will need to substitute it into the function in order to find the corresponding y-coordinate.

·         When you are finished, plot the points from your table and draw the parabola.

o   REMEMBER – both sides of the parabola should be mirror images of each other… if this is not the case with your parabola, you’ve done something wrong.

o   If you are asked to show the axis of symmetry, it is an imaginary (dashed) vertical line that passes through the vertex of the parabola.

 
 
EXAMPLES WITH EXPLANATIONS:                   (Click on images to enlarge)

 
 
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