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Graphing Quadratic Functions 1 - Locating the Vertex

 
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)      There are three common forms of the equation of a quadratic function:

·         Vertex form:              y = a(xh)2 + k

·         Standard form:         y = ax2 + bx + c

·         Intercept form:         y = a(xp)(xq)

 
When graphing a parabola, the first step is to locate and plot the vertex.
 
HOW TO LOCATE THE VERTEX – EQUATION IN VERTEX FORM:
 
1)      The x-coordinate is the OPPOSITE of the constant term of the binomial inside of the parentheses.

2)      The y-coordinate is the SAME as the constant term being added (generally to the right) to the squared expression.  If no such term can be seen, the   y-coordinate of the vertex is 0.

 
EXAMPLES WITH EXPLANATIONS:            (Click on image to enlarge)

  


 

HOW TO LOCATE THE VERTEX – EQUATION IN STANDARD FORM:

 

1)      Use the formula: -b / 2a to determine the x-coordinate of the vertex

2)      Substitute this value into the function and evaluate in order to determine the y-coordinate of the vertex.

 

EXAMPLES WITH EXPLANATIONS:            (Click on images to enlarge)

  

 

 

 

 
HOW TO LOCATE THE VERTEX - EQUATION IN INTERCEPT FORM:
 

1)      The x-coordinate is halfway between p  and  q.

2)      Substitute this value into the function and evaluate in order to determine the y-coordinate of the vertex.

 
EXAMPLES WITH EXPLANATIONS:            (Click on images to enlarge)
 

 

 

 
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