Quadratic Equations - Finding the Coordinate of The VertexHello,   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...

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

Asked on by maythany

2 Answers | Add Yours

lfryerda's profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted on

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).

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

 The reason why it is 1,2 is because you need to set the parenthesis equal to 0, which you didn't seem to do.

x-1=0

  +1 +1

   x=1

You solved it right just the last part was a bit off

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