Questions: 12. Standard Form of Quadratic Function Explain the advantage of writing a quadratic function in standard form.

Solution Steps

The question asks for an explanation rather than a computational solution, so it doesn't require a Python code solution. However, if you have a computational question related to quadratic functions, feel free to ask!### Step 1: Understanding the Standard Form of a Quadratic Function

A quadratic function is typically expressed in the form \( ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \neq 0 \). This is known as the standard form of a quadratic function.

1. Identifying the Coefficients: The standard form makes it easy to identify the coefficients \( a \), \( b \), and \( c \), which are essential for various calculations, such as finding the vertex, axis of symmetry, and roots of the quadratic equation.

2. Using the Quadratic Formula: The standard form is directly used in the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) to find the roots of the quadratic equation. This formula is derived from the standard form, making it straightforward to apply.

3. Determining the Direction of the Parabola: The sign of the coefficient \( a \) in the standard form immediately tells us whether the parabola opens upwards (\( a > 0 \)) or downwards (\( a < 0 \)).

4. Calculating the Discriminant: The discriminant \( b^2 - 4ac \) is easily calculated from the standard form, which helps determine the nature of the roots (real and distinct, real and equal, or complex).

5. Graphing the Function: The standard form provides a clear starting point for graphing the quadratic function, as it allows for easy calculation of the vertex and axis of symmetry.

Final Answer