Quadratic Equations - Finding the Coordinate of The Vertex



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? 



Expert Answers

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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, 


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).

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