Quadratic Equations - Finding the Coordinate of The Vertex

Hello,

 

I am given  `y=5x^2-10x+7` and I must change it to the form of 

`y=a(x-h)^2+k` . So I've already done this and the answer is `5(x-1)^2+2` 

For the coordinates I wrote -1,2 but the answer is 1,2. I don't understand this and how do you get the vertex coordinate? what do I need to look for? 


Thanks,


MB

Expert Answers

An illustration of the letter 'A' in a speech bubbles

There are two reasons for converting a quadratic function from standard form `y=ax^2+bx+c` to vertex form `y=a(x-h)^2+k` .  Either you are trying to solve for x for a specific y-value (usually zero) or you are trying to find the vertex of the parabola (either to help with graphing or find a maximum or minimum).

In this case, you are trying to find the vertex.

If a parabola is in vertex form `y=a(x-h)^2+k` , then the vertex is `(h,k)` .  Notice that the h-value is the opposite sign of what is inside the brackets.

This means that in your case, 

`y=5(x-1)^2+2`

has a vertex at (1,2).  Take the number inside the brackets, and change the sign.  That is, -1 changes to 1 for the x-value of the vertex.  The y-value of the vertex is the last number of the vertex form, in this case 2.

The vertex of the parabola is (1,2).

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial