Question

What is the vertex of the graph of y = x² + 4x?
(-2, -12)
(-2,-8)
(-2,-6)
(-2,-4)

Answer 1

Answer:

(-2,-4)

Step-by-step 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 $d=\frac{-b}{2a}$ so I substitute$d=-\frac{4}{2*1} =-2$

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