Question

What is the vertex of `y=x^2+9x+8`?

Answer 1

Vertex is `(-9/2,-49/4)`.

Explanation:

For finding vertex of the equation, we should convert it in the form `(y-k)=(x-h)^2`, where `(h,k)` is the vertex.

As `y=x^2+9x+8`

= `x^2+2×9/2×x+(9/2)^2-(9/2)^2+8`

= `(x+9/2)^2-81/4+8`

= `(x+9/2)^3-49/4`

i.e. `y+49/4=(x+9/2)^2`

or `(y-(-49/4))=(x-(-9/2))^2`

Hence, vertex is `(-9/2,-49/4)`.

graph{x^2+9x+8 [-15.08, 4.92, -12.72, -2.72]}