#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

• Graph this function on your calculator.

#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

• Graph the function on your calculator.

#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

• Graph the function on your calculator.