Mastering Quadratic Functions: Understanding the Quadratic Parent Function for Accurate Graphs

Quadratic Parent Function

Domain: [0, ∞) Range: [0, ∞)

The quadratic parent function is the simplest quadratic function of the form f(x) = x^2. This is also known as a parabola in the Cartesian plane. The graph of the quadratic function is a U-shaped curve called a parabola.

The quadratic parent function is also characterized by certain features, such as the vertex, axis of symmetry, and direction of opening. These features can help with graphing any quadratic function.

– Vertex: The vertex is the point where the parabola changes direction. The vertex is located at the point (0,0) for the quadratic parent function.

– Axis of symmetry: The axis of symmetry is a line that divides the parabola into two equal parts. The axis of symmetry for the quadratic parent function is the y-axis, which is also the x = 0 line.

– Direction of opening: The quadratic function can either open upward or downward. The quadratic parent function opens upward.

Overall, the quadratic parent function serves as a basis for understanding other quadratic functions and their respective graphs. By understanding the vertex, axis of symmetry, and direction of opening of the parent function, we can easily graph any other quadratic function by applying appropriate transformations.

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