Understanding Quadratic Functions: Exploring the Function f(x) = x^2 and its Graph

f(x)=x^2

The function f(x) = x^2 represents a quadratic function

The function f(x) = x^2 represents a quadratic function. In this case, the variable x is squared, which means that you multiply x by itself.

Let’s break down the function and see how it works:

The input of the function, x, can be any real number. When you substitute a value for x into the function, such as f(2), you replace every x in the expression with that value.

For example, if we evaluate f(2):

f(2) = (2)^2 = 2 * 2 = 4

So, f(2) = 4. This means that when x is equal to 2, the function output is 4. In other words, if you graph the function, the point (2, 4) will be on the graph.

You can evaluate the function for any value of x. For instance, if we evaluate f(-3):

f(-3) = (-3)^2 = (-3) * (-3) = 9

So, f(-3) = 9. This means that when x is equal to -3, the output of the function is 9. The point (-3, 9) will be on the graph of the function.

Additionally, you can also find the vertex of the parabola that represents the function f(x) = x^2. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b/2a. In this case, a = 1 and b = 0, so the vertex is at x = 0.

Plugging in x = 0 into the function f(x) = x^2, we have:

f(0) = (0)^2 = 0 * 0 = 0

Therefore, the vertex is located at (0, 0).

In summary, the function f(x) = x^2 represents a quadratic function where the output is the square of the input value. The graph is a parabola that opens upwards, with the vertex at the origin (0, 0).

More Answers: