Question

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

Answer 1

Answer:

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

Step-by-step 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).