What is a quadratic function?
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A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
What is the parent function of a quadratic function?
A quadratic function is a polynomial function of degree 2. It is in the form of f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to zero. The graph of a quadratic function is a parabola, which can be either concave up or concave down, depending on the value of the leading coefficient, a.
To understand quadratic functions in more detail, we can follow these steps:
1. Start with the definition: A quadratic function is a polynomial function of degree 2.
2. Note the general form: The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.
3. Observe the coefficient 'a': The coefficient 'a' determines the shape and direction of the quadratic function. If a > 0, the parabola opens upwards (concave up). If a < 0, the parabola opens downwards (concave down).
4. Study the coefficient 'b': The coefficient 'b' represents the linear term in the quadratic function. It affects the symmetry and position of the parabola.
5. Analyze the constant term 'c': The constant term 'c' is the y-intercept of the quadratic function, which indicates where the parabola intersects the y-axis.
By following these steps, we have gained an understanding of what a quadratic function is and its general form.