Addition, subtraction signs, brackets, squares and powers, square roots and roots, fractions. Random variables are also used, like x.
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In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
Graphing
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If they are quadratic equations then if their discriminant is less than zero then they have no solutions
You will apply them when solving quadratic equations in which the quadratic expression cannot be factorised.