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How to write an equation for a parabola in vertex form

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3 Answers

Some examples for the formula
 
The format of the equation that shows you where the vertex is
 
y = a(x - h)2 + k
 
Example.  This parabola has a vertex at (3,4).
 
y = 2(x - 3)2 + 4
 
Example 2.  This parabola has a vertex at  (1,1)
 
y = (x–1)² + 1
 
 
How to find "a"???
 
Pick a point on the graph other than the vertex.  Let's say you see the line pass through (1,5) and the vertex is at (3,4)...
 
 
First the vertex gives you this...
 
y = a (x - 3)2 + 4
 
Put the values (1,5) into this equation.
 
 
5 = a (1 - 3)2 + 4
 
Solve for a
 
5 = a*(-2)2 + 4
5 = 4a + 4
1 = 4a
1/4 = a
 
Final equation is
 
y = 1/4*(x - 3)2 + 4
The vertex form of a parabola's equation is generally expressed as : 
 
y=a(x−h)^2+k Where (h,k) is the max or min.
 

1.      Look at the graph.  
2.      Find the vertex of the graph (h,k)
3.      Vertex is the highest / lowest point of the graph known as Max or min  (h,K) 
 
Plug this into the form y=a(x−h)^2+k  Next solve for "a"
 
4.      To find the "a "  ----> pick a point on the graph other than vertex.  (usually y intercept)
5.       plug it into the vertex form and slove for "a"
 
 

IF the general equation is given for the graph: y=ax^2+bx+c, then 
 
1.       to find the vertex: use formula x= -b/2a
2.       plug x into the given equation to find y value
3.       now you have (h,k)  
4.       find a point on the graph and plug in to the vertex form equation to find "a"
 
 
see below for example
y= x^2-2x+3 given: x= -b/2a ------> x= -(-2)/2(1)= 1-----> pug this into the given equation so y= 2
 
Min (1,2) and now pick x=0 so y=3 (0,3) to find "a"----->  in this case a = 1
y=a(x−h)^2+k    
y=(x−1)^2+2
 
 


Hi Aliyah,
I am in AZ too.
To write an equation for a parabola in vertex form, you need to read the coordinates of the vertex from the given graph as (h, k) first. You can write
y = a(x-h)^2 + k
Now, read the y-intercept or any other given point.
y-int = ah^2+k
You can solve for a,
a = (y-int-k)/h^2
So, the vertex form is y = [(y-int-k)/h^2](x-h)^2 + k