Question

What are the coordinates of the vertex of the parabola with the equation y = x2 + 2x – 3?

A
(-1, -4)

B
(1, -4)

C
(3, -4)

D
(-3, 12)

Answer 1

A. (-1, -4)

Explanation:

The vertex can be found by converting the equation from standard form to vertex form.

Vertex

Considering the x-terms, we have ...

y = (x^2 +2x) -3

where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...

y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2

y = (x +1)^2 -4

Compare this to the vertex form equation ...

y = a(x -h)^2 +k

which has vertex (h, k).

We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).

On the attached graph, the vertex is the turning point, the minimum.