What is the Axis of Symmetry for the Function F(X) = 7−4X+X2? X = –3 X = –2 X = 2 X = 3
The axis of symmetry for the function F(x) = 7−4x+x^2 is x = -2. This is determined by finding the x-value of the vertex, and since the function is in the form of f(x) = ax^2 + bx + c, the axis of symmetry is given by x = -b/2a.
The axis of symmetry is a critical concept in understanding the behavior of a quadratic function. It represents the line that divides the parabola into two symmetrical halves. In this case, the axis of symmetry at x = -2 indicates that the parabola is symmetric around this vertical line.
Identifying the axis of symmetry helps in graphing the function and finding the vertex of the parabola. Additionally, it is significant for determining the maximum or minimum value of the function. Understanding how to calculate the axis of symmetry is fundamental in analyzing and interpreting quadratic functions.
Understanding Axis Of Symmetry
Definition: The axis of symmetry is a vertical line that divides a quadratic function into two equal halves.
Importance: Finding the axis of symmetry helps determine the vertex of a quadratic function and provides valuable insight into its shape and behavior. It enables us to quickly identify various key properties such as the maximum or minimum value of the function.
For the given function F(x) = 7−4X+X2, we can determine the axis of symmetry by using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -4.
Plugging these values into the formula, we get:
| Value of x | Axis of Symmetry |
|---|---|
| x = -3 | x = 2.5 |
| x = -2 | x = 2 |
| x = 2 | x = 2 |
| x = 3 | x = 2.5 |
Therefore, the axis of symmetry for the given function is x = 2.
Deriving The Axis Of Symmetry
The axis of symmetry for the function F(X) = 7−4X+X2 can be derived by identifying the coefficients and applying the formula. To find the axis of symmetry, we need to determine the value of X that represents the line of symmetry in the parabolic graph. In the given function, the coefficient of the quadratic term X2 is 1, the coefficient of the linear term -4X is -4, and the constant term is 7. Using the formula X = -b/2a, where a is the coefficient of the quadratic term and b is the coefficient of the linear term, we can calculate the axis of symmetry. By substituting the values, we find that the axis of symmetry is X = -(-4) / (2 1) = 2. Therefore, the function F(X) = 7−4X+X2 has an axis of symmetry at X = 2.
Finding The Axis Of Symmetry For F(x) = 7−4x+x2
When finding the axis of symmetry for the function F(X) = 7−4X+X2, it is essential to identify the coefficients of the quadratic equation, which in this case are a = 1, b = -4, and c = 7. Applying the axis of symmetry formula, you will use the equation X = -b / (2a) to find the X-coordinate of the vertex. Solving for X yields the axis of symmetry as X = -b / (2a), which is a crucial step in understanding the properties of the given quadratic function.
Determining The X Values Of The Axis Of Symmetry
The axis of symmetry for the function F(X) = 7−4X+X2 is calculated by using the formula X = -b/(2a) where a = 1 and b = -4. Substituting the values, we get X = -(-4)/(21) = 2. This means that the axis of symmetry is at X = 2. Therefore, the axis of symmetry for the given function is X = 2. This point divides the parabola into two symmetrical halves.
Conclusion
To find the axis of symmetry for the function F(x) = 7 – 4x + x^2, we can use the formula x = -b/2a. By plugging in the values of a, b, and c from our original equation, we can calculate that the axis of symmetry is x = -2.
This means that the graph of the function is symmetric around the vertical line x = -2. This information is crucial for accurately graphing the function and understanding its behavior.