quadratic function
A quadratic function is a type of polynomial function with degree 2
A quadratic function is a type of polynomial function with degree 2. It can be defined by an equation of the form:
f(x) = ax^2 + bx + c
Where a, b, and c are constants.
The graph of a quadratic function is a parabola. The coefficient “a” determines the direction of the parabola. If “a” is positive, the graph opens upwards (concave up), and if “a” is negative, the graph opens downwards (concave down).
The vertex of the parabola is an important point on the graph. It represents the minimum or maximum value of the function, depending on whether the parabola opens upwards or downwards. The x-coordinate of the vertex can be found using the formula:
x = -b / (2a)
To find the y-coordinate of the vertex, you can substitute the x-coordinate into the equation for f(x), which will give you the value f(x) = f(-b / (2a)).
Quadratic functions can also be used to solve real-world problems, such as finding the maximum or minimum of a function, determining the height of an object thrown into the air, or finding the dimensions that optimize a certain area.
To solve quadratic equations (equations that set a quadratic function equal to zero), there are several methods available, including factoring, completing the square, and using the quadratic formula:
x = (-b ± √(b^2 – 4ac)) / (2a)
This formula will give you the solutions (roots) of the quadratic equation, which may be real or complex numbers.
Overall, understanding quadratic functions is crucial in many areas of mathematics and science. It allows us to model and analyze a variety of phenomena, solve problems, and make predictions.
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