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Quadratic Expressions
Quadratic equations are a type of mathematical equation that describes curved lines, known as parabolas. They are used to describe many phenomena in sciences, such as the movement of objects due to gravity. Quadratic equations have interesting properties, which makes them interesting to analyze from a mathematical perspective, and lend the equations very well to being used to solve problems in the real world.
Forms of Quadratic Equations
Quadratic equations can be expressed in different forms, which can be used to determine different properties of the system.
Basic information about quadratic expressions, and how these can be analyzed, and their significance in math and science.
The standard form of the quadratic expression which only includes nxz, nx, and n expressions.
The factored form of the quadratic expression describes where the quadratic expression crosses the x axis, and is in the form of multiplying brackets together.
The vertex form of the quadratic expression describes where the midpoint of the expression is on the coordinate graph.
Converting Between Quadratic Forms
Different forms of quadratic equations can be converted between one another to solve problems involving quadratic equations
Converting from the standard form to the factored form by factorization.
Converting from the factored form to the standard form using the FOIL method.
Converting from the standard form to the vertex form by completing the square.
Converting from the vertex form to the standard form by multiplying out the square term.
Converting from the factored form directly to the vertex form to find the vertex from the roots.
Converting from the vertex form to the factored form to identify the roots of an equation in the vertex form.
More Complex Conversions
More complex quadratic equations require more complex techniques to solve them than the above listed methods.
Sometimes, very complex quadratic expressions can be simplied by using the technique of finding the greatest common factor, and from there deriving a simpler, easier to analyze quadratic expression.
Factoring equations in the standard form that have a values that are not 1 by decomposition. This is a good alternative to finding the greatest common factor.
The quadratic formula is a powerful equation which can be used to determine the roots of a quadratic equation in the standard form. It has a lot of versatile applications for analyzing quadratic expressions.
Some quadratic expressions are in forms which are unclear, but can nevertheless be analyzed using the same techniques as for analyzing other quadratic expressions.