Question

State where the graph of the parabola is increasing and where it is decreasing.

y=x^2 - 10x
A. Increasing from -[infinity] to 5, decreasing from 5 to [infinity]
B. Increasing from -[infinity] to 0, decreasing from 0 to [infinity]
C. Increasing from -[infinity] to 10, decreasing from 10 to [infinity]
D. Increasing from -[infinity] to 2.5, decreasing from 2.5 to [infinity]

Answer 1

The graph of the parabola is increasing from -infinity to 2.5 and decreasing from 2.5 to infinity.

Step-by-step explanation:

To determine where the graph of the parabola is increasing or decreasing, we need to examine the coefficient of the x-term in the equation y = x^2 - 10x.

The coefficient of x^2 is 1, which means the parabola opens upwards. If the coefficient of x^2 is positive, then the graph is increasing on the intervals where x is less than the vertex, and decreasing on the intervals where x is greater than the vertex.

So, the correct answer is D. The graph is increasing from -infinity to 2.5, and decreasing from 2.5 to infinity.