y = x² + 4x
First thing you do is decide, is it opening up or down. Quadratics are usually in the form Ax² + Bx + c = 0
Check if the A value is positive or negative. If it is positive, then the parabola opens up.
Then find the intercepts. This one is very easy because the x factors out like so
0 = x(x + 4)
x = 0 or x = -4
Therefore this function has x-intercepts at x = 0 and x = -4
Then complete the square in order to find the vertex. This is where you take the B value, divide it by two and then square the result.
0 = x² + 4x
B = 4
4/2 = 2
2² = 4
Then add and subtract this value to the function like so
0 = (x² + 4x + 4) - 4
The blue part is where you add the result and the red if where you subtract the result (this is just to keep the function equivalent).
then you complete the square of what you have within the brackets.
0 = (x + 2)² - 4
Thus the vertex of this parabola is (-2,-4)