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Vertex Form
By
Dan Zuniga & Andrew Poage

A School (Castro’s Room), Afternoon
A shot of a long hallway is seen. Through the door of a classroom, single student is taking a test
His name is Randy, and he is taking a test on graphing quadratics in vertex form.
The teacher is pacing back and forth
Teacher
So, one more time. Vertex form is a method of graphing that exists in the form:
The Teacher rights the form on the board y=a(xh)^2+k
Teacher
A vertex is the highest or lowest point on a graph. The vertex form can tell us that point on the graph.
The teacher turns to face the board
Teacher
Not all quadratics start in vertex form. Take this, for example.
y=x^24x+4. We can convert this to y=(x2)^2, and then graph
Teacher graphs the problem
Teacher
Are you paying attention, Mister Loage?
Randy looks up at the board, POV
Randy
Yes.
Teacher
Good, then solve the following for me.
POV as Randy turns the pages of his test (made so that it looks like a disabled person made it)
Teacher
1st Problem.
Graph y=(x+2)^2+3
Randy
Alright… so I am gonna write out the base equation (writes down y=a(xh)^2+k) Now I gotta remember, the H equals the xcoordinate of the vertex, and the K equals the Y coordinate of the vertex. And since it is minus H in the base equation, if in the problem it is plus H, the x is negative. Now to start the problem, I see that H is plus 2, so that means the xcoordinate of the vertex is 2. Now for the ycoordinate, the K is plus 3, so that means the ycoordinate is 3, time to plot it. (Plots vertex on graph) Good, now to plot the rest of the graph like it is x^2, since there is no amplifier to the equation. (Graphs rest of equation) Perfect.
Teacher hits Randy’s knuckles with a ruler
Teacher
Nice. Now, go on.
Randy rubs his eyes, and flicks away a tear
Teacher
What’s wrong?
Randy
Nothing, just...34 zeroes...Anyways, the next problem says
Randy reads the next problem, it reads “3(x1)^22”
Randy
Hmm… a little bit tougher, but no biggie. So first thing to do is the same thing as before, that 3 in the front doesn’t affect the vertex, so I see that the H is 1, so that means x=1. And then I see that K is 2, which means y=2. (Plots vertex on graph) Alright, now I just gotta graph the rest like it is 3x^2 from the vertex. (Graphs the equation like so) Ah excellent… another one done.
Teacher is writing the phrase “I am not a real teacher” 15 or 20 times on the board
Randy
(Wiping away forehead tears) Alright, onto the next one.
Teacher
HEY! Eyes on your own paper!
Randy
There’s no one else here…
(mutters)
Dumbass…
Teacher
So, like, okay. I’m feeling where ya at?
Randy
Yeah. So, the next one is actually a conversion, and then a graph…
Teacher is jumping from one desk to another
ECU of Randy sweating profusely from all of his orifices
Randy reads the next problem, to which it says x^2+8x+15
Randy
I don’t remember Vasquez teaching me this… but I guess I gotta try… (Readies pencil) So it says I gotta convert to vertex form and graph, so let's start by converting this. First thing I gotta do is move the 15 to the outside by completing the square, so what I do is I take B, which is 8, divide it by 2 and square it, which equals 16. So now below this I write (x^2+8x+16)+15, now I have the 15 on the outside. Next, I have to subtract 16 which I got from completing the square from 15 (writes 16 next to 15). Now all I have to do is factor the equation in parentheses and combine like terms and I’ll be good! I know that the function in parentheses is (x+4)^2 so I can turn it into that, then 1516 equals 1, so our final equation is y=(x+4)^21! Now time to graph… I see that the vertex is (4,1) since H is 4 and K is 1. And now we plot the rest like it is x^2 since there is no amplifier!
Randy
Um, this one. The last question. I...I don’t know if I can do this!
Teacher
Come on, Randy. I believe that you can. But it’s not enough for me to do that. You need to believe in yourself.
Randy
Well, I don’t.
Teacher
Randy, we gotta finish this movie. Make it happen!
Randy
Okay. Okay
Randy is back to crying like a bitch
Randy
This problem is… 3x^26x1… oh boy. So just like the previous problem, I need to get the 1 out, and in addition, I need to take out the 3. First things first let’s get rid of the 1 in order to begin complete the square so now it will look like this (3x^26x)1. Now I gotta get rid of that 3, so what I am going to do is factor it out like this, and now the function looks like 3(x^2+2x)1. Now to complete the square, I must take B again, divide it by 2, and square it, and since B is 2, the completed square is 1, so now the function looks like this 3(x^2+2+1)1. Also like in the previous problem, I have to subtract the completed square by the outside value, but since there is a 3 on the outside, I have to multiply the subtracted value by 3, so now the function is 3(x^2+2x+1)11(3). When the value is multiplied it becomes positive 3 and when added to 1 it becomes positive 2. Then all I do is factor the equation in the parentheses and I’m done! This function factored is (x+1)^2, so that means the final function in vertex form is y=3(x+1)^2+2. So now that I have it in vertex form I can graph (Graphs equation).
Teacher is staring intently at the board as Randy finishes his problem
Randy
(waiting with bated breath)
Teacher
Mr. Loage...You’re excused.
Randy runs out, then jumps in the air like the end of Rocky (ur the best around) as music plays, and time stands still.
END MOVIE
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