 Site Navigation                          Graphs of Quadratic Functions

Examples #1: Graph • Step 1: Find the vertex.  So the vertex is at (-3, -1)
• Step 2: Find the roots.
Start with Next, factor the function , set its factors equal to zero, and solve for x.  or Telling us that x = -4 and x = -2
• Step 3: Determine if the parabola opens up or down.
Since the coefficient of is positive 1, the parabola opens up.
• Step 4: Find other points to fill in the graph of x y -2 0 -1 3 0 8 1 15  #2: Graph • Step 1: Find the vertex.  So the vertex is (1, 1)
• Step 2: Find the roots.
Since does not factor, we must use the quadratic formula.    The approximate values of roots are x = 0.42 and x = 1.58.
• Step 3: Determine if the parabola opens up or down.
Since the coefficient of is negative 3, the parabola opens down.
• Step 4: Find other points to fill in the graph of .
 x y 1 -11 0 -2 1 1 2 -2 3 -11  #3: Graph • Step 1: Find the vertex.  So the vertex is • Step 2: Find the roots.
Since does not factor, we must use the quadratic formula.    These are imaginary roots and the parabola does not touch or cross the x–axis.
• Step 3: Determine if the parabola opens up or down.
Since the coefficient of is positive 2, the parabola opens up.
• Step 4: Find other points to fill in the graph of .
 x y -1 2 0 3 1 3 2 7 3 15 S Taylor

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