Question

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

Answer 1

The coordinates of the vertex are (-1,-4).

Explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

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

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

We are given the function:

`y=x^2+2x-3`

We must transform the equation above by completing squares:

The first two terms can be completed to be the square of a binomial. Recall the identity:

`x^2+2xy+y^2=(x+y)^2`

Thus if we add and subtract 1:

`y=(x^2+2x+1)-3-1`

Operating:

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

The trinomial in parentheses is a perfect square:

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

Adding 4:

`y+4=(x+1)^2`

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).

The coordinates of the vertex are (-1,-4).