Question

How do you find the VERTEX of a parabola `y=x^2+7x+12`?

Answer 1

Use the method of completing the square to convert to vertex form and get the vertex at `(-7/2, -1/4)`

Explanation:

Vertex form: `y=m(x-a)^2+b` with vertex at `(a,b)`

`y=x^2+7x+12`

`rarr y= x^2+7x+(7/2)^2+12 -(7/2)^2`

`rarr y = (x+7/2)^2 + (48/4 - 49/4)`

`rarr y = (x- (-7/2))^2 + (-1/4)`

`color(white)("XXXXXX")`which is the vertex form with the vertex at `(-7/2,-1/4)`