What is "if f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x?

Okay, here's some information about the functions f(x) = –x² + 3x + 5 and g(x) = x² + 2x, formatted in Markdown and including the specified links:

Given the functions f(x) = –x² + 3x + 5 and g(x) = x² + 2x, we can explore several concepts:

*   **Function Evaluation**: We can evaluate each function for a specific input value. For example, f(2) = –(2)² + 3(2) + 5 = -4 + 6 + 5 = 7.  Similarly, g(2) = (2)² + 2(2) = 4 + 4 = 8.  More generally, we are substituting a value for 'x' to calculate the resulting output of the function. This is related to the concept of [function%20evaluation](https://www.wikiwhat.page/kavramlar/function%20evaluation).

*   **Function Operations**: We can perform arithmetic operations on these functions, such as addition, subtraction, multiplication, and division. For instance, (f + g)(x) = f(x) + g(x) = (–x² + 3x + 5) + (x² + 2x) = 5x + 5. We can also subtract, leading to (f - g)(x) = f(x) - g(x) = (-x² + 3x + 5) - (x² + 2x) = -2x² + x + 5.  These operations combine the two functions together. These ideas lead to discussions about [function%20operations](https://www.wikiwhat.page/kavramlar/function%20operations).

*   **Finding Roots (Zeros)**:  The roots or zeros of a function are the values of *x* for which f(x) = 0 or g(x) = 0. For f(x) = –x² + 3x + 5, we would need to solve the quadratic equation –x² + 3x + 5 = 0. For g(x) = x² + 2x, we can factor it as x(x + 2) = 0, which gives us roots x = 0 and x = -2.  Solving for roots utilizes the [quadratic%20formula](https://www.wikiwhat.page/kavramlar/quadratic%20formula).

*   **Vertex of a Parabola**: Both f(x) and g(x) are quadratic functions, meaning their graphs are parabolas. We can find the vertex of each parabola.  For f(x), the x-coordinate of the vertex is given by -b/2a = -3/(2*(-1)) = 3/2. The y-coordinate is f(3/2) = -(3/2)² + 3(3/2) + 5 = -9/4 + 9/2 + 5 = 29/4.  For g(x), the x-coordinate of the vertex is -2/(2*1) = -1. The y-coordinate is g(-1) = (-1)² + 2(-1) = 1 - 2 = -1.  The vertex is a key feature when considering [parabola%20properties](https://www.wikiwhat.page/kavramlar/parabola%20properties).

*   **Composition of Functions**:  We can compose the functions, such as f(g(x)) or g(f(x)). For example, f(g(x)) = f(x² + 2x) = -(x² + 2x)² + 3(x² + 2x) + 5.  The other composition can be calculated in a similar fashion. [Function%20composition](https://www.wikiwhat.page/kavramlar/function%20composition) enables creating more complex functions.