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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.

Q: Which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring?

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The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.

The slope of your quadratic equation in general form or standard form.

Whether the equation has 2 distinct roots, repeated roots, or complex roots. If the determinant is smaller than 0 then it has complex roots. If the determinant is 0 then it has repeated roots. If the determinant is greater than 0 then it has two distinct roots.

Unless the operands form an arithmetic sequence, it is not at all simple. That means the difference between successive points must be the same. If that is the case and the SECOND difference in the results is constant then you have a quadratic.

imaginary

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The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.

The quadratic formula is famous mainly because it allows you to find the root of any quadratic polynomial, whether the roots are real or complex. The quadratic formula has widespread applications in different fields of math, as well as physics.

Factorise it!

Whether or not that there is a solution to a quadratic equation,

If it doesn't have an equal sign, then it's an expression, not an equation. The expression 7x2x is quadratic, because it equals 14x², and something is quadratic if it contains the squared exponent ².

solutions

discriminant

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The slope of your quadratic equation in general form or standard form.

Somebody (possibly in seventh-century India) was solving a lot of quadratic equations by completing the square. At some point, he noticed that he was always doing the exact same steps in the exact same order for every equation. Taking advantage of the one of the great powers and benefits of algebra (namely, the ability to deal with abstractions, rather than having to muck about with the numbers every single time), he made a formula out of what he'd been doing:The Quadratic Formula: For ax2 + bx + c = 0, the value of x is given byThe nice thing about the Quadratic Formula is that the Quadratic Formula always works. There are some quadratics (most of them, actually) that you can't solve by factoring. But the Quadratic Formula will always spit out an answer, whether the quadratic was factorable or not.I have a lesson on the Quadratic Formula, which gives examples and shows the connection between the discriminant (the stuff inside the square root), the number and type of solutions of the quadratic equation, and the graph of the related parabola. So I'll just do one example here. If you need further instruction, study the lesson at the above hyperlink.Let's try that last problem from the previous section again, but this time we'll use the Quadratic Formula:Use the Quadratic Formula to solve x2 - 4x - 8 = 0.Looking at the coefficients, I see that a = 1, b = -4, and c = -8. I'll plug them into the Formula, and simplify. I should get the same answer as before:

Just like any other equation, you can set up a table of x values, and calculate the corresponding y values. Then plot the points on the graph. In this case, it helps to have some familiarity with quadratic equations (you can find a discussion in algebra books), and recognize (from the form of the equation) whether your quadratic equation represents a parabola, a circle, an ellipse, or a hyperbola.