Quadratic Parent Function
The quadratic parent function, also known as the basic quadratic function, is a simple form of a quadratic equation
The quadratic parent function, also known as the basic quadratic function, is a simple form of a quadratic equation. It can be represented as:
f(x) = ax^2 + bx + c
Where:
– f(x) represents the output or the y-value of the function.
– x represents the input or the x-value.
– a, b, and c are constants that determine the shape, position, and orientation of the quadratic function.
The graph of a quadratic parent function is a U-shaped curve known as a parabola. The direction in which the parabola opens depends on the value of the coefficient a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.
The vertex of the quadratic parent function is an important point on the parabola. It can be found using the formula:
Vertex = (-b/2a, f(-b/2a))
The axis of symmetry of the parabola is a vertical line that passes through the vertex, dividing the parabola into two equal halves.
The basic quadratic function can have different properties based on the values of the coefficients a, b, and c.
1. The coefficient a determines the steepness of the curve. A larger value of a causes the parabola to be narrower, while a smaller value makes the parabola wider.
2. The coefficient b determines the horizontal shift of the parabola. If b is positive, the parabola shifts to the left, and if b is negative, it shifts to the right.
3. The constant term c determines the vertical shift of the parabola. If c is positive, the parabola shifts upward, and if c is negative, it shifts downward.
The quadratic parent function serves as the foundation for studying more complex quadratic equations, such as those involving transformations, translations, and scaling of the basic parabola. It is a fundamental concept in algebra and provides a framework for solving real-world problems that can be modeled with quadratic functions.
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