Question

1. # Over Which Interval Is The Graph Of F(X) = –X2 + 3X + 8 Increasing?

## Introduction

Understanding the concept of increasing and decreasing intervals of a graph is an important mathematical skill to have. Knowing when a graph is increasing or decreasing can help you in solving many problems and make it easier to understand the overall pattern of a function. In this article, we will discuss what it means for a graph to be increasing or decreasing, and then apply that knowledge to the specific example of the graph F(x) = −x2 + 3x + 8. We will also explore how such concepts can be used more broadly in mathematics.

## The graph of F(x)

The graph of F(x) is increasing over the interval [-1, 1].

## The interval over which the graph is increasing

Assuming we are talking about the interval of a graph on the x-axis, the graph is increasing over the interval between -1 and 1. So, if we take any two points within that range, such as -0.5 and 0.5, the line will be going up as it passes through those points.

## Conclusion

In conclusion, the graph of F(x) = –x2 + 3x + 8 is increasing over the interval (-∞, 2]. This result was obtained by calculating the critical points and then analyzing where the tangent line to each point had a positive slope. Analyzing functions like this can be difficult at first but with practice it becomes easier. As always, graphing tools are also helpful when trying to determine whether or not a function is increasing or decreasing on a given interval.

2. Have you ever wondered over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?

Well, if you have, you’re in luck! Today, we’re going to dive into the details and figure out exactly where this graph is increasing.

To get started, let’s quickly review what we need to know about a graph in order to determine whether it is increasing or decreasing. A graph is increasing if the slope of the graph is positive; conversely, a graph is decreasing if the slope is negative.

Now, let’s take a look at the graph of f(x) = –x2 + 3x + 8. We can see that this graph is a parabola, and its slope can be determined by taking the derivative of the equation. The derivative of this equation is –2x + 3, which is positive when x is less than 3/2.

Therefore, the graph of f(x) = –x2 + 3x + 8 is increasing on the interval (-∞, 3/2]. Notice that the endpoint of this interval is included in the interval, so the graph is increasing from negative infinity up to 3/2.

Pretty cool, right? Now that we know the answer to this question, you can use this same method to determine when other graphs are increasing or decreasing.

Thanks for joining me today as we explored the graph of f(x) = –x2 + 3x + 8 and figured out when it is increasing!