Quadratic Parent Function
Domain: [0, ∞) Range: [0, ∞)
The quadratic parent function is the simplest quadratic function, also known as the standard quadratic function or the parent quadratic function. It is written in the form of f(x) = x².
The graph of this function is a parabola, which is a U-shaped curve. It passes through the origin (0,0), and the vertex of the parabola lies on the y-axis at the point (0,0).
The axis of symmetry of the parabola is the y-axis, which means that the left and right sides of the parabola are mirror images of each other.
When graphing a quadratic function using the parent function, the key feature to note is the a value in the quadratic equation, which determines the shape of the parabola. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.
To graph a quadratic function, we can use the vertex form of the equation, which is f(x) = a(x-h)² + k, where (h,k) is the vertex of the parabola. We can use this form of the equation to find the vertex, the axis of symmetry, and the direction that the parabola opens.
Overall, understanding the quadratic parent function is important for understanding quadratic functions in general and is useful for solving problems in various fields, such as physics, engineering, and economics.
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