Graphing Tips for Every Type of Quadratic Function

Does graphing make you want to scream?  For many students, IT DOES!

I hear you.  

Graphing can be difficult at first, but I’m going to walk you through it.

In Algebra 1, there are 2 main ways you’ll have to graph:  vertex form and standard form. 

{Here’s a hint:  Vertex form is way easier!}

But you have to know how to graph in standard form as well, so I have tips for you.

There is a third way that some students have to learn…intercept form.

Don’t worry, I have a video for that, too.

Graphing in Standard Form

“Negative b over 2a” is an odd sort of formula, but it’s super important in finding the vertex when you’re in standard form.

The steps, briefly, are…

1. State the a, b, and c.
2. Plug into the negative b over 2a formula (see video).  That’s the x-value of the vertex.
3. Plug the answer you got in Step 2 to the equation and solve.  That’s the y-value of the vertex.
4. Plot the vertex on a coordinate plane.
5. Take the x-value of the vertex and subtract 1 to it and then add 1 to it.  Plug those numbers into the equation and get two new points.  Plot these points.
6. If the a value of the original equation was positive, the graph opens up.  If it was negative, the graph opens down.
7. The Axis of Symmetry (AOS) is written x = a number.  That number is the x-value of the vertex.

Step 4 is a little tricky.  The video should help with that.

Watch to see an example.

Graphing in Vertex Form

Now that you’ve graphed in standard form, vertex is relatively simple.

Remember to always use the opposite number of what is inside the parentheses (), and you should do just fine.

Here are the general steps…

1.  The x-value of the vertex is the opposite of the number inside the parentheses (e.g., -3 becomes 3).
2. They y-value is the number at the end.  Keep the sign of the number.
3. Plot the vertex on a coordinate plane.
4. Take the x-value of the vertex and subtract 1 to it and then add 1 to it.  Plug those numbers into the equation and get two new points.  Plot these points.
5. If the a value of the original equation was positive, the graph opens up.  If it was negative, the graph opens down.
6. The Axis of Symmetry (AOS) is written x = a number.  That number is the x-value of the vertex.

Notice that only the first two steps are different.  After that, it’s the same as graphing in standard form.

Graphing in Intercept Form

These problems look different right from the beginning.  Don’t let that throw you off.

Generally, here are the basic steps:

1. Write the opposite number of what’s inside the parentheses and put it in a coordinate point like this…(the number, 0). Do the same with the other parentheses.  Plot these two points.  They’re both on the x-axis.
2. Find the x-value that’s halfway between the two points you just plotted.  Plug that number into the function and solve.  These two numbers are your vertex.  Plot the vertex.
3. If the a value of the original equation was positive, the graph opens up.  If it was negative, the graph opens down.
4. The Axis of Symmetry (AOS) is written x = a number.  That number is the x-value of the vertex.

The video works through one of these problems.

You can always find even more help from Algebra Student by clicking on the links in the menu at the top of the page.

You’ve got this!