Question

What is the y positive and y negative for the graph of y = x^2 - 4x?

Option 1: y positive is all values of y greater than or equal to 0, and y negative is all values of y less than 0.
Option 2: y positive is all values of y greater than 4, and y negative is all values of y less than 4.
Option 3: y positive is all values of y greater than 2, and y negative is all values of y less than 2.
Option 4: y positive is all values of y greater than -4, and y negative is all values of y less than -4.

Answer 1

The graph of the equation y = x^2 - 4x represents a quadratic function. The positive values of y are greater than -4, and the negative values of y are less than -4.

Step-by-step explanation:

The graph of the equation y = x^2 - 4x represents a quadratic function. To find the positive and negative values of y, we need to analyze the behavior of the graph.

First, let's find the vertex of the parabola by completing the square.

The equation can be rewritten as y = (x^2 - 4x + 4) - 4, which simplifies to y = (x - 2)^2 - 4. The vertex is at (2, -4).

Since the parabola opens upwards, the values of y will be positive when they are greater than the y-coordinate of the vertex, which is -4.

Therefore, y positive is all values of y greater than -4.

The values of y will be negative when they are less than the y-coordinate of the vertex.

Therefore, y negative is all values of y less than -4.