Honglan R. answered • 03/25/20
Writing A College Algebra Reference Book, Apply Educational Psychology
There are 3 methods to find vertex.
Method one:
Here is how to find vertex.
If the problem has following form: f(x)=ax2+ bx + c
Then, vertex form is: f(x)=a(x-h)2+ k
answer for Vertex is: v=(h, k), interpretation is that when x value is h, y value is k; this is where vertex is.
y=(x+2)(x-6)
y=x2– 4x -12
y=(x2– 4x) -12 (Recall perfect square of trinomial)
b= -4, and (b/2)2=4
y=(x2– 4x+4)-4 -12 (added 4, then subtracted 4)
y=(x-2)2-4-12
y=(x-2)2-16
At this point, I have the equation in vertex form f(x)=a(x-h)2+ k
answer for Vertex is: v= (h, k),
Therefore, v= (2, -16)
Method 2:
y=(x+2)(x-6)
y=x2– 4x -12
a=1, b=-4,
x= - b/(2a)=2, value 2 is h value in v= (h, k).
plug x=2 to the original equation, which is y=(x+2)(x-6). You get y=-16.
Now, you get v= (2, -16).
Method 3:
y=(x+2)(x-6)
find x intercept. Graph pass At x=-2, x=6. Other way to think this is as graph pass at point (-2, 0) and (6, 0).
Now, here is something other people might not teach you.
y=(x+2)(x-6)
y=x2– 4x -12, The function is parabola. Therefore, we need to find middle point between -2 and 6. Between -2 and 6 is x coordinate of the vertex, which is x=2. Therefore, I get v= (2, ?).
plug x=2 to “original” function y=(x+2)(x-6) to get y=-16
Therefore, v= (2, -16)
Note: It is good idea that always plug value into “original” function in case at some point you make some mistake, then you keep making mistakes.
Now, let’s find x intercepts.
y=(x+2)(x-6)
x intercepts occur when y=0. Hence, there are two x intercepts in this equation, at x=-2 and x=6. Other way of express this is (-2, 0) and (6, 0)
*** obviously find x intercept is easier.
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