![]() ![]() Read the roots where the curve crosses or touches the x-axis.Choose arbitrary values of x and y to plot the curve.Given a quadratic equation, rewrite the equation by equating it to y or f(x).To graph a quadratic equation, here are the steps to follow: Hence, x = 2 ± 1.5i How to Graph a Quadratic Equation? ⇒ √ (−9) = 3i where i is the imaginary number √−1 In this case, the discriminant is negative:Īccording to the standard form of a quadratic equation ax 2 + bx + c = 0, we can observe that Solve the quadratic equation below using quadratic formula:Ĭomparing the problem with the general form of quadratic equation ax 2 + bx + c = 0 gives,Ĭomparing with the quadratic equation, we get, Substitute the values in the quadratic formula Use the quadratic formula to find the roots of x 2-5x+6 = 0.Ĭomparing the equation with the general form ax 2 + bx + c = 0 gives, Let’s solve a few examples of problems using the quadratic formula. And, if the discriminant is negative, then the quadratic equation has no real root. When the discriminant value is zero, then the equation will have only one root or solution. A quadratic equation has two different real roots of the discriminant. The discriminant is part of the quadratic formula in the form of b 2 – 4 ac. The roots of a quadratic equation depend on the nature of the discriminant. The above two values of x are known as roots of the quadratic equation. The presence of the plus (+) and minus (-) in the quadratic formula implies that there are two solutions, such as: Isolate the term c to right side of the equation We can derive the quadratic formula by completing the square as shown below. Suppose ax 2 + bx + c = 0 is our standard quadratic equation. From these examples, you can note that, some quadratic equations lack the term “c” and “bx.” How to use the quadratic formula? In a quadratic equation, the variable x is an unknown value, for which we need to find the solution.Įxamples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc. The term second degree means that at least one term in the equation is raised to the power of two. ![]() What is a Quadratic Equation?Ī quadratic equation in mathematics is defined as a polynomial of second degree whose standard form is ax 2 + bx + c = 0, where a, b and c are numerical coefficients and a ≠ 0. Before we can dive into this topic, let’s recall what a quadratic equation is. In this article, we will learn how to solve quadratic equations using two methods, namely the quadratic formula and the graphical method.
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