## Quadratic Function

### A quadratic function is a polynomial function of degree 2, meaning it has the form:

f(x) = ax^2 + bx + c

where a, b, and c are constants, and a is not equal to zero

A quadratic function is a polynomial function of degree 2, meaning it has the form:

f(x) = ax^2 + bx + c

where a, b, and c are constants, and a is not equal to zero. The highest power of x in the function is 2, hence the term quadratic.

The graph of a quadratic function is a U-shaped curve called a parabola. It can open upwards if the coefficient of the x^2 term (a) is positive, or downwards if a is negative. The vertex of the parabola is the lowest or highest point depending on the direction of the parabola. The axis of symmetry is a vertical line passing through the vertex, and the vertex is the point where the axis of symmetry intersects the parabola.

The constant term c represents the y-intercept, which is the point where the parabola intersects the y-axis. The linear term bx determines the slope of the parabola at different points. If b is positive, the parabola opens to the right, and if b is negative, it opens to the left.

Quadratic functions have various applications in algebra, physics, engineering, and other fields. They can be used, for example, to model the trajectory of a projectile, describe the shape of a satellite dish, or analyze the profit or cost function of a business.

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