x-squared – y = -x...VERTEX?

Question

instructions: what is the vertex and coordinates?


questions:
1. x-squared – y = -x
2. y = x-squared + 2x - 6



thanks..^_^

Answer 1

The vertex is (h, k) in the equation:
y = a(x - h)^2 + k

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

The vertex is (- 1/2, - 1/4).

I'm not sure which "coordinates" you are talking about.... There are a lot of them.

2)
y = x^2 + 2x + 6
y = x^2 + 2x + 1 + 6 - 1
y = (x + 1)^2 + 5

Vertex is (-1, 5)

Answer 2

Try to complete a square
1) y= x^2+x =(x+1/2)^2 -1/4 you´ll see tha on the curve(parabola)
its minimum value is reached when x+1/2=0 (because (x+1/2)^2 is always>=0
So the vertex is(-1/2,-1/4)

2) y =(x+1)^2 -7 So V(-1,-7)