This document provides instruction on graphing quadratics. It begins by outlining what students should already know, like the definition of a quadratic and what a vertex is. It then covers how to graph quadratics in vertex form, zeroes form, and standard form. For each form, it explains how to identify the vertex or zeroes, make an x-y table of values, and graph the parabola. Examples are worked through and practice problems are provided for students to try. Bonus materials at the end demonstrate how to graph on a calculator and find the vertex. The goal is for students to learn how to graph a quadratic from any of the three common forms.

1. Graphing Quadratics
with
Ms. Schwartz
pssstt…press the speaker!
Graphing Quadratics

2. Graphing Quadratics
Things you should know already…
• What a quadratic is.• What a quadratic is.
• What the vertex is.
Just a heads up, you should be taking notes on graph
paper, I mean, you already knew that it is called
“Graphing Quadratics.”

3. Graphing Quadratics
Things you should know by the
end…
• How to graph a quadratic from
all three forms.
• The three basic forms of the
equation of a quadratic.

4. Graphing Quadratics
Know what you want? Go for it!
Vertex
Form
GraphingIdentifying Forms
Standard
Form
Zeroes Form
Already been through the lessons?
Practice one of the following
Don’t know where to start?
It’s cool, just click here.
HINT: Use the left/right
arrows to navigate through
the lessons or the menu bar
at the bottom to switch
between them
HINT: This button will always
bring you back to this slide
Bonus Material!

5. Graphing Quadratics
Vertex Form
The Basics
So here the vertex is
It’s important to notice that
the signs switch that is
because the original
equation has minus signs in
front of h and k.
So here the vertex is
You should also notice that
the a out in front does not
effect the vertex.
Vertex StandardZeroes Form
Go to….

6. Vertex Form
Let’s Practice
Identify the Vertex Press over arrow to reveal
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

7. Vertex Form
Creating an x-y table
Once you know your vertex you are going to want to
create an x-y table.
x y
-1
0
1 6
2
3
Put your vertex in the middle
then fill in your x column by
going two numbers in each
direction.
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

8. Creating an x-y table
Once you know your vertex you are going to want to
create an x-y table.
x y
-3 -10
-2 -7
-1 -6
0 -7
1 -10
Fill in your y-values by
plugging in for x.
For example:
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

9. Graphing from an x-y table
Now you have 5 points. Graph them!
x y
-3 -10
-2 -7
-1 -6
0 -7
1 -10
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

10. Bam!
You’re done.
Your can now graph from vertex form.
Well, maybe you should try one more.
Try it first. The answer is on the next page.
Graphing QuadraticsVertex StandardZeroes Form
Go to….

11. x y
1 10
2 4
3 2
4 4
5 10
Vertex Practice!
Graphing QuadraticsVertex StandardZeroes Form
Go to….

12. Zeroes Form
The Basics
So here the zeroes are
It’s important to notice that
the signs switch because
you are setting x – 3 = 0
and solving for x to find the
zeros.
So here the zeroes are
You should also notice that
the a out in front does not
effect the zeroes.
Graphing QuadraticsVertex StandardZeroes Form
Go to….

13. Zeroes Form
Let’s Practice
Identify the Zeroes Press over arrow to reveal
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

14. Zeroes Form
Let’s Practice
Graphing QuadraticsStandardZeroes Form
Go to….
Because a parabola is
symmetric the x- coordinate of
the vertex is exactly halfway
between the x-coordinates of
the two zeroes . So, you want
to find the average of the two
zeroes.
To find the y-coordinate you
plug the xv in to the original
equation and solve for yv.
So the vertex is (1, 36).
Vertex

15. Creating an x-y table
Once you know your vertex you are going to want to
create an x-y table.
x y
-5 0
0 -35
1 -36
2 -35
7 0
Fill in your y-values by
plugging in for x.
For example:
Graphing QuadraticsStandardZeroes Form
Go to….
HINT: Use your zeroes in
your x-y table. Its like getting
two free points!
Vertex

16. Graphing from an x-y table
Now you have 5 points. Graph them!
Graphing QuadraticsStandardZeroes Form
Go to….
x y
-5 0
0 -35
1 -36
2 -35
7 0
Vertex

17. Kazam!
You’re done.
Your can now graph from zeroes form.
Well, maybe you should try one more.
Try it first. The answer is on the next page.
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

18. x y
-8 0
0 16
-2 18
-4 16
4 0
Zeroes Practice!
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

19. Graphing QuadraticsStandardZeroes Form
Go to….
Standard Form
The Basics
Some Examples
Vertex

20. Graphing QuadraticsStandardZeroes Form
Go to….
Standard Form
Finding the vertex
To find the x coordinate
of the vertex you will use
the equation:
Vertex is:
To find the y-coordinate you plug the xv in to the
original equation and solve for yv.
Vertex

21. Creating an x-y table
Once you know your vertex you are going to want to
create an x-y table.
x y
0 -6
1 3
2 6
3 3
4 -6
Fill in your y-values by
plugging in for x.
For example:
Graphing QuadraticsStandardZeroes Form
Go to….
HINT: Remember quadratics
are symmetric!
Vertex

22. Graphing from an x-y table
Now you have 5 points. Graph them!
Graphing QuadraticsStandardZeroes Form
Go to….
x y
0 -6
1 3
2 6
3 3
4 -6
Vertex

23. Yahoo!
You’re done.
Your can now graph from standard form.
Well, maybe you should try one more.
Try it first. The answer is on the next page.
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

24. x y
-1 2
0 -10
1 -14
2 -10
3 2
Standard Form Practice!
Graphing QuadraticsStandardZeroes Form
Go to….
Vertex

25. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Identifying Forms Practice
Each slide will have 1 equation. Write down the
equation and form you think it is then hit the over
arrow to reveal the form.

26. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Vertex form

27. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Standard form

28. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Vertex form

29. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Vertex form
But move the 5 over and it’s standard.

30. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Zeroes Form

31. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Standard form
Notice in this one b=0.

32. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Zeroes Form

33. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Standard form
or Vertex Form

34. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Zeroes Form

35. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Nice Practice!
Did you get them all?
If not, take a minute and note down
why you missed what you missed.
Now, head back home and either practice graphing or
review another section!

36. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Graphing
Under the first hidden area will be the x-y table.
Under the second will be the graph.
Also, remember there is a link at the bottom if you
need to go back and review.

37. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
x y
-3 0
-1.5 5.25
-.5 -6.25
.5 5.25
2 0
Check your
x-y table
Check your
graph

38. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
x y
1 0
2 -6
3 -8
4 -6
5 0
Check your
x-y table
Check your
graph

39. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
x y
0 1
-1 13
-2 17
-3 13
-4 1
Check your
x-y table
Check your
graph

40. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
x y
-2 13
-1 10
0 9
1 10
2 13
Check your
x-y table
Check your
graph

41. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
x y
1 -6
0 3
-1 6
-2 3
-3 -6
Check your
x-y table
Check your
graph

42. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
x y
-2 13
-1 10
0 9
1 10
2 13
Check your
x-y table
Check your
graph

43. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
x y
1 4/3
2 1/3
3 0
4 1/3
5 4/3
Check your
x-y table
Check your
graph

44. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Nice Job!
Want some Bonus Materials?
Graphing on
your calculator.
Review with
outside sources!
Finding the
vertex on your
Calculator.

45. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Bonus Materials
Graphing on your Calculator
Click on the video below to start

46. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Review with outside sources!
This is an awesome video
showing someone graphing
one quadratic in each form.
This is Purple Math’s page
on graphing quadratics.
This is Khan Academy’s
review of graphing in all
forms.
(This one is interactive.)

47. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
Bonus Materials
Finding the Vertex on your calculator
Click on the video below to start

48. Graphing QuadraticsVertex StandardZeroes Form
If you can’t remember or need a refresher head back to any of the sections.
That’s it!
If you’ve made through all the practice and
all the units you are done!
Thanks for being awesome!