The document provides examples of graphing quadratic functions by: 1) Creating an x-y table of values to plot points for functions like y=x^2, y=2x^2, y=-x^2, etc. 2) Plotting the points on a graph and identifying the vertex (lowest or highest point) and axis of symmetry (line splitting the graph in half). 3) Working through examples like y=x^2, y=2x^2, y=1/2x^2, y=-x^2, y=x^2-4, y=-x^2-2, y=2x^2-4 to demonstrate how to graph

2. Problems
0 Problem 1: Graph y = x2
0 Problem 2: Graph y = 2x2
0 Problem 3: Graph y = ½x2
0 Problem 4: Graph y = -x2
0 Problem 5: Graph y = x2 - 4
0 Problem 6: Graph y = -x2 - 2
0 Problem 7: Graph y = 2x2 - 4

3. Problem 1
0 Graph y = x2

4. Problem 1
0 Graph y = x2
The first thing we need to do is to remember the x and y
table we used to make for y = mx + b. We will do this on
the below table always using the numbers -2, -1, 0, 1, 2.
X Y On the next page you will see how
the table looks completed. Our
-2 problem is y = x2. We will do the
-1 problem by taking a number on the
side of the x and place it in the x
0 place of the problem. The answer of
1 this will go in the y problem place.
2

5. Problem 1
0 Graph y = x2
X Y
Now we need to graph the
-2 4
problem. We will make our
-1 1
marking points using the x in the
0 0
x axis and the y in the y axis. The
1 1
graph will be on the next page.
2 4

6. Now we need to find the
axis of symmetry (my
graph is not perfect, so
we must imagine it is
completely equal in its
line lengths) and the
vertex.

7. The vertex is green. This is
We must remember that the
the vertex because it is the
axis of symmetry is the line
lowest part of the graph
that splits the graph
that does not go onward. If
completely in
the parabola was flipped
half, imagining my graph
then the vertex would be
was perfect, our axis of
the highest part because it
symmetry would be directly
wouldn’t have lines going
in the middle. From now on
onward. From now on this
this presentation I shall
presentation I shall make
make the axis of symmetry
the vertex green.
purple.

8. Problem 2
0 Graph y = 2x2

9. Problem 2
0 Graph y = 2x2
Now we must use our table again and get points which
we will plot.
X Y
-2
-1
0
1
2

10. Problem 2
0 Graph y = 2x2
Now we must graph this and find the vertex and axis of
symmetry.
X Y
-2 8
-1 1
0 0
1 1
2 8

13. Problem 3
0 Graph y = ½x2

14. Problem 3
0 Graph y = ½x2
We will again use the table and then graph. We will find
the vertex and axis of symmetry again.
X Y X Y
-2 -2 4
-1 -1 ½
0 0 0
1 1 ½
2 2 4

17. Mini Lesson
There is no such thing as negative 0. If you
were to
have a problem like –(0)2. The answer would
not
be -0, but only 0 as zero trumps all.

18. Problem 4
0 Graph y = -x2

19. Problem 4
0 Graph y = -x2
Now we need to make a table again, and then find the
vertex and line of symmetry.
X Y When you replace the x and
put a number in its place we
-2 will make the problem (using
-1 r as an example) look like –
0 (r)2. We will remember
PEMDAS as we do this.
1
2

20. Problem 4
0 Graph y = -x2
Now we need to make a table again, and then find the
vertex and line of symmetry.
X Y X Y X Y
-2 -2 -(-2)2 -2 -4
-1 -1 -(-1)2 -1 -1
0 0 -(0)2 0 0
1 1 -(1)2 1 -1
2 2 -(2)2 2 -4

22. The vertex is in the
highest position as it
is the place where
lines do not go
onward.

23. Problem 5
0 Graph y = x2 – 4

24. Problem 5
0 Graph y = x2 – 4
Now we need to make a table again, and then find the
vertex and line of symmetry.
X Y X Y
-2 -2 0
-1 -1 -3
0 0 -4
1 1 -3
2 2 0

27. Problem 6
0 Graph y = -x2 + 2

28. Problem 6
0 Graph y = -x2 + 2
X Y X Y
-2 -2 -2
-1 -1 1
0 0 2
1 1 1
2 2 -2

31. Problem 7
0 Graph y = 2x2 - 4

32. Problem 7
0 Graph y = 2x2 – 4
Now we need to make a table again, and then find the
vertex and line of symmetry.
X Y X Y
-2 -2 4
-1 -1 -2
0 0 -4
1 1 -2
2 2 4