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Exploring Quadratic Graphs  Problem 3
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Graphing an equation like this is a little tricky, because there is a whole lot of things being done to x. You need to be really careful with the order of operations, when you’re doing your substitution. So it told me to make a table, I’m going to choose some x values. Personally, I tend to make a lot of mistakes with negatives, I don’t know about you. So I’m going to start with x equals 0 and I’ll go from there.
If my x value was 0, my y number would be 0 take away 3. That’s 3² to +9 plus 1 is 10, that’s the first point in my table. Then if I try 1, 1 take away 3 is 2² is 4, plus 1 is 5. 2 take away 3 is 1, 1 times itself is +1 plus 1 again. 1, 2 I’m just moving along with my x numbers.
If I plug in x equals 3, I’ll have 0² plus 1. If I plug in 4, 4 take away 3 is 1² plus 1 is 2. I’m happy because I started to find that symmetry. This 2 showed up again, so I know without having to do any more Math, how to complete my table. 5 is going to be here, 6 is going to be here, matched up with my next consecutive x numbers 4, 5, 6.
These problems even though they involve a lot of Math here in the equation, they can be filled in pretty quickly when you use shortcuts of symmetry. The last thing I know before I start making my graph, is that I’m going to have the Vertex point 3,1. So let’s get these dots on the graph.
I’m going to start with 0,10. So 0 is my side to side number and 10 is my up and down number 0, 1, 2 , 3, 4, 5, 6, 7, 8, 9, 10 that’s my y intercept. My next point was (1,5) 1, 2, 3, 4, 5. (2, 2) then I have my Vertex 3,1. That Vertex is really important because that’s where I’m going to introduce my Axis of Symmetry and start putting dots on there without having to count any more.
This vertical line that goes right through my Vertex is not on the parabola, but it helps me graph these other dots. Like this guy is one away from the Axis of Symmetry, same height. The same thing here, equally as high but 2 away, 3 away, boom, those are the points from my table. I know and I didn’t even have to count them, then I can draw my parabola that connects it. I missed that point, but you guys get the idea.
The way this is useful is because symmetry can make these graphs go a lot more quickly. Your teacher will be impressed also, if you can describe how you created this table, not by doing it all out one by one, but by doing patterns and symmetry. They not only show up in the table, but they also show up in the graph. It will make your homework be a lot more quick.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
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Sample Problems (6)
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Exploring Quadratic Graphs
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Problem 2 5,343 viewsMake a table and graph:
y = x² − 2 
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Problem 3 4,730 viewsMake a table and graph:
y = (x − 3)² + 1 
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Problem 4 746 views 
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Problem 5 707 views 
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Problem 6 649 views
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Tom · 7 months, 2 weeks ago
:) I will leave it to other viewers to find her mistake in the table which she does not however repeat when doing the graph. HINT: symmetry reveals the error.