Examples
#1: Graph
• Step 1: Find the vertex.

So the vertex is at (-3, -1)
• Step 2: Find the roots.

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