Quadratic Function
f(x) = x^2
A quadratic function is a function that can be written in the form of f(x) = ax² + bx + c, where a, b, and c are constants, and x is the variable. The graph of a quadratic function is a parabola, which opens upwards or downwards, depending on the sign of the leading coefficient a.
The quadratic function has many important features. The x-intercepts of a quadratic function can be found by setting f(x) equal to zero and solving for x. The quadratic formula can be used to find the x-intercepts, which are also called roots or zeros of the function.
The vertex of a quadratic function is the point on the graph where the parabola changes direction. The vertex is also the maximum or minimum value of the function, depending on the direction of the parabola. The x-coordinate of the vertex can be found using the formula: x = -b/2a.
The axis of symmetry is the vertical line that passes through the vertex of the parabola. The equation for the axis of symmetry is x = -b/2a.
The discriminant of a quadratic function is b² – 4ac. The discriminant can be used to determine the number and type of roots of the function. If the discriminant is positive, the function has two real roots. If the discriminant is zero, the function has one real root (which is also the vertex). If the discriminant is negative, the function has two complex roots.
Overall, the quadratic function is a very important function in mathematics and has many useful applications in various areas like physics, engineering, and economics.
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