Question

What is the vertex of the graph of y = x² + 4x?

(-2, -12)
(-2,-8)
(-2,-6)
(-2,-4)

Answer 1

(-2,-4)

Explanation:

in this exercise I have the formula of the parable expressed as:

`y=ax^(2) +bx+c`

I can write it in its "vertex form"

`y=a(x-d)^(2) +e` being (d,e) the coordinates of the vertex of said parabola.

by clearing the equation I can see that
`d=(-b)/(2a)` so I substitute
`d=-(4)/(2*1) =-2`

Now taking d as the value for the x axis of the vertex coordinate, I substitute d in x, in the initial equation

`y=x^(2) +4x =(-2)^(2)+4(-2)=4-8=-4`

So finally, I have the coordinates of the vertex of the parabola are (-2,-4)

Done