Question

1. # Which Is The Graph Of F(X) = X2 – 2X + 3?

Have you ever wondered what a graph of the equation F(X) = X2 – 2X + 3 looks like? If so, you’ve come to the right place. In this article, we are going to take a look at what the graph of this equation looks like and how it can be used to solve equations with polynomials. We will also discuss how F(X) = X2 – 2X + 3 can be manipulated in order to represent different equations. So if you’re curious about what the graph of this equation is, read on!

## The graph of f(x) = x2 – 2x + 3

The graph of f(x) = x2 – 2x + 3 is a parabola that opens upward and has a vertex at (1, 2). The y-intercept is 3, and the x-intercepts are -1 and 2.

## The different types of graphs of f(x) = x2 – 2x + 3

The graph of f(x) = x2 – 2x + 3 is a parabola. It has two roots, one at x = 1 and one at x = 3. The y-intercept is at (0, 3). The graph is symmetric about the y-axis.

To find the equation of the axis of symmetry, we need to find the value of x that makes f(x) = 0. This happens when x = 2. So, the axis of symmetry is the line x = 2.

The graph opens up because the leading coefficient, a, is positive. This can be seen by looking at the sign of the discriminant, b2 – 4ac. In this case, b2 – 4ac = 4 – 12 = -8. This means that there are no real roots and the graph will not intersect the x-axis.

## How to find the equation of the graph of f(x) = x2 – 2x + 3

There are a few steps that you need to follow in order to find the equation of the graph of f(x) = x2 – 2x + 3. First, you need to identify the points on the graph where the function changes from increasing to decreasing, or vice versa. These points are called turning points. There are two turning points on the graph of f(x) = x2 – 2x + 3. They are located at (1,2) and (3,-4).

Next, you need to determine the concavity of the graph at each turning point. The concavity can be either positive or negative. To determine concavity, you take the second derivative of the function at each turning point. The second derivative of f(x) = x2 – 2x + 3 is f”(x) = 2*x – 2. At (1,2), we have f”(1) = 0, so the concavity is indeterminate. At (3,-4), we have f”(3) = 6, so the concavity is positive.

Now that we know the locations and concavities of the turning points, we can write down the equation of the graph. The general form for a quadratic function with two turning points is y = a(x-h)(x-k)+c, where (h,k) are the coordinates of one turning point and c is the y-intercept of the graph. In this case, we have (h,k) = (1,2) and c = 3, so our equation is y = (x-1)(x-3)+3. This is the equation for the graph of f(x) = x2 – 2x + 3.

## The pros and cons of the graph of f(x) = x2 – 2x + 3

There are a few things to consider when looking at the pros and cons of the graph of f(x) = x2 – 2x + 3. On the one hand, the graph is a parabola, which means it is smooth and symmetrical. Additionally, the vertex of the graph is at (1,2), which is a nice, easy-to-remember point. On the other hand, the graph does not have any intercepts, which could make it difficult to use in certain situations.

## Conclusion

In conclusion, understanding the graph of a function can be an essential part of mathematics. The graph of F(x) = x2 – 2x + 3 is a parabola with its vertex at (1,2), and it opens up from left to right. The more we understand how these graphs work, the better equipped we will be when it comes to solving equations and making calculations in real-world problems. Therefore, take some time to get familiar with this particular graph and become comfortable with reading graphs in general.