Question

What is the x- coordinate of the vertex of the graph that represents y= (x+1) (x+5) explain how you know?

Answer 1

-3

Explanation:

To find the x-coordinate of the vertex of the graph representing the equation y = (x + 1)(x + 5), we can start by recognizing that the given equation is in the form of a quadratic function, specifically a quadratic trinomial. A quadratic function is represented by a parabola, and the vertex of the parabola represents its minimum or maximum point.

The general form of a quadratic trinomial is y = ax^2 + bx + c, where a, b, and c are constants. In this case, our equation y = (x + 1)(x + 5) can be expanded to y = x^2 + 6x + 5. By comparing this equation with the general form, we can see that a = 1, b = 6, and c = 5.

The x-coordinate of the vertex of a quadratic function is given by the formula x = -b/2a. Plugging in the values from our equation, we have x = -6 / (2 * 1) = -6/2 = -3.

Therefore, the x-coordinate of the vertex of the graph representing y = (x + 1)(x + 5) is -3.

Answer 2

-3

Explanation:

Since we know that x = -1 or x = -5 when y = 0, the x-coordinate of the vertex must be between the roots of the parabola. The average of -1 and -5 is -3.