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using the quadratic formula or the graphics calculator.

Yes, you can do it another way, by using a new method, called Diagonal Sum Method, that can quickly and directly give the 2 roots, without having to factor the equation. This method is fast, convenient and is applicable to any quadratic equation in standard form ax^2 +bx + c = 0, whenever it can be factored. It requires fewer permutations than the factoring method does, especially when the constants a, b, and c are large numbers. If this method fails to get answer, then consequently, the quadratic formula must be used to solve the given equation. It is a trial-and-error method, same as the factoring method, that usually takes fewer than 3 trials to solve any quadratic equation. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009)

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Q: Can you solve a quadratic equation without factoring?
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How do you do a parabola?

A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.


What is the quadratic formula for?

The quadratic formula is used to solve the quadratic equation. Many equations in which the variable is squared can be written as a quadratic equation, and then solved with the quadratic formula.


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Here are two ways to know if a given quadratic equations can be factored (can be solved by factoring). 1. Calculate the Discriminant D = b^2 - 4ac. When D is a perfect square (its square root is a whole number), then the given equation can be factored. 2. Solve the equation by using the new Diagonal Sum method (Amazon e-book 2010). This method directly finds the 2 real roots without having to factor the equation. Solving usually requires fewer than 3 trials. If this method fails to get the answer, then we can conclude that the equation can not be factored, and consequently the quadratic formula must be used.


Why do you use square roots to solve quadratic equations?

Because it's part of the quadratic equation formula in finding the roots of a quadratic equation.