Question

How do you find the coordinates of the vertex `y= 2x^2 + 7x - 21`?

Answer 1

Vertex is `(-7/4,-217/8)` or `(-1 3/4,-27 1/8)`

Explanation:

To find the coordinates of vertex of `y=2x^2+7x-21`, one should convert this equation into vertex form i.e.

`(y-k)=a(x-h)^2`, where vertex is `(h,k)`

Now `y=2x^2+7x-21`

`hArry=2(x^2+7/2x)-21`

`=2(x^2+2xx7/4xx x+(7/4)^2-(7/4)^2)-21`

`=2((x+7/4)^2-(7/4)^2)-21`

`=2(x+7/4)^2-2xx49/16-21`

`=2(x+7/4)^2-49/8-21`

`=2(x+7/4)^2-217/8`

or `(y+217/8)=2(x+7/4)^2`

Hence, vertex is `(-7/4,-217/8)` or `(-1 3/4,-27 1/8)`

graph{2x^2+7x-21 [-6, 4, -28.56, -8.56]}