The answer to “What is the square root of a negative number?” will be a topic for another time. Recall that the discriminant belongs inside the square root of the second term, but what is the square root of a negative number? If we plot this quadratic equation on a graph we see that the parabola never touches the x-axis, so when D<0, the parabola has no roots. If you take a good look at both formulas, you will notice that the quadratic formula and its variation both contain b2-4ac. Below is a picture representing the graph of y x + 2x + 1 and its solution. Just substitute a,b, and c into the general formula: a 1 b 2 c 1. Use the formula to solve theQuadratic Equation: y x 2 + 2 x + 1. That of the discriminant being negative, D<0. Example of the quadratic formula to solve an equation. ![]() Now the last case is the most perplexing, and simple at the same time. We can see this as D became smaller, the two roots converged into one. What Does the Factored Form of a Quadratic Tell You Next, let’s now consider why factored form is useful. Substitute the values in the quadratic formula. Comparing the equation with the general form ax 2 + bx + c 0 gives, a 1, b -5 and c 6. Use the quadratic formula to find the roots of x 2 -5x+6 0. To learn more about this, read our detailed review article on the quadratic formula. Let’s solve a few examples of problems using the quadratic formula. Once you have the quadratic formula and the basics of quadratic equations down cold, its time for the next level of your relationship with parabolas: learning about their vertex form. To do so, we must identify the values of a, b, and c. It is a single point where the vertex just touches the x-axis. One method for solving a quadratic equation is to use the quadratic formula. This will make the second term of the quadratic equation equal to zero, so our roots will now look like: The second case is that of a discriminant of zero, D=0. Starting with the general quadratic form: ![]() In the end, I’m sure will agree with my sentiments that the Quadratic Formula is one of the most useful formulas for solving a quadratic equation.We will demonstrate a simple quadratic formula proof. On the following slides, you will begin practicing to use the Quadratic Formula to SOLVE quadratic equations. ![]() We will also look at a few questions where we will first need to simplify the equation by either multiplying polynomials, collecting like terms, or multiplying by the least common multiple before plugging into this beloved formula. In the video below, we’ll walk through countless examples of how to successfully apply the quadratic formula given a quadratic equation so we can arrive at the correct roots (i.e., zeros or x-intercepts or solutions). ![]() Next, we simply plug in these values into the formula and simplify.
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