One thing you guys probably already know about graphs is that they’re useful in lots of ways, but sometimes they’re not very useful. Like if you had a vertex that was a fractional value, it’d be really hard to look at a graph and be able to tell what fraction was being represented. That’s why it’s really important that you know how to find the vertex algebraically as well as how to find it graphically.
So let’s go with this problem to find the vertex, I’m going to start by figuring out what my x coordinate is, -b/2a. In our case I’ll have -3 over 2 times 1 which is -3/2, that’s going to be the x coordinate of my vertex. To find the corresponding y value, I’m going to have to substitute that fraction back in. Y is going to be -3/2 squared plus 3 times -3/2 plus 4. I can already tell this is common denominator coming on. -3/2 times itself is 9/4, 3 times 3/2 is -9/2 there and then plus 4.
In order to do that addition, I need to find the common denominator, so this first fraction I’m going to leave is 9/4, the second guy I’m going to turn into -18/4, and then this I’m going to turn into 16/4, and that was good because now I can just look at the numerator add across the top from left to right. 9 take away 18 is -9 plus 16 is+7, so my y value is going to be 7/4. This is my vertex right here.
I could verify that by looking at a graph to just make sure that it’s somewhere in between the x values -1 and -2 and somewhere in between the y values, of +1 and +2.
The next thing this problem asked me to do is to write the equation for the Axis of Symmetry, but don’t worry it’s not hard we’ve pretty much already done it. Remember the equation for the Axis of Symmetry looks like x equals -b/2a. It’s a line and -b/2a is how I found that coordinate. So my Axis of Symmetry is the line x equals -3/2, that’s a vertical line that goes right up and down through my parabola. The Axis of Symmetry is really helpful when you’re graphing points.
Experience the 'A-Ha!' moment with the best teachers
whom we hand-picked for you!
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.... :)”
“You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”