This is true no matter the values of a, b, and c. You can always use the quadratic formula to solve a quadratic equation. Can You Always Use The Quadratic Formula? Thus, the graph never intersects the x-axis (y = 0). Note that there is no zero, since there are two complex conjugate roots. This is the graph of the parabola from the quadratic y = x 2 + x + 1. We have coefficient values of a = 1, b = -3, and c = 2. This equation is already in quadratic standard form. Example 1: Two Distinct Real Solutions (Positive Discriminant)Ĭonsider the quadratic equation x 2 – 3x + 2 = 0. We’ll start with 2 distinct real solutions (a positive discriminant). Let’s look at some examples to see how the quadratic formula works in 3 different cases. Finally, work to simplify the values in the formula until we cannot reduce any further.Now, rewrite the quadratic formula with the values of a, b, and c substituted.Then, write out the general quadratic formula, without any values plugged in.Sometimes it helps to write them somewhere to avoid missing any negative signs. Next, identify the values of a, b, and c.You may need to rearrange terms and combine like terms to do so. First, get the equation into quadratic standard form, ax 2 + bx + c = 0.Using the quadratic formula is straightforward with a little practice if you follow the steps: How To Use The Quadratic Formula (Solving Quadratic Equations) You can learn more about when to use the quadratic formula here. Dealing with gravity and falling objects in physics problems.This is helpful when factoring is difficult. Finding the roots of a quadratic equation.This is helpful to find 1 or 2 “base points” to graph when sketching a parabola (unless the solutions are complex conjugates). Locating the zeros (x-intercepts) of a parabola.After combining like terms and making one side of the equation zero (quadratic standard form), we can solve using the quadratic formula. Solving a polynomial equation of degree 2.There are many scenarios when you might want to use the quadratic formula: Remember that in the third case, our complex conjugates have the form r + si and r – si (here, s is not zero, so the two complex conjugate solutions are distinct). It also gives us an idea of what the graph (a parabola) looks like. The discriminant of a quadratic tells us the nature of the solutions.
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