Like if i was givin a graphed parabola how would i figure out how to write the equation, in vertex form/

## 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}+ kExample. This parabola has a vertex at (3,4).

y = 2(x - 3)

^{2}+ 4Example 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}+ 4Put the values (1,5) into this equation.

5 = a (1 - 3)

^{2}+ 4Solve for a

5 = a*(-2)

^{2}+ 45 = 4a + 4

1 = 4a

1/4 = a

Final equation is

y = 1/4*(x - 3)

^{2}+ 4The 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