What is one of the most useful and versatile formulas in all of mathematics?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
The Quadratic Formula!
We have already looked at three major ways to solve a quadratic equation:
- Factoring
- Square Roots
- Completing The Square
But there is a formula that will work every time!
And it’s derived using the method of completing the square, which means all of these solving techniques are integrally related.
But why is the quadratic formula so special?
Because, as not only is it super easy to use but as Purple Math accurately states, while we may not always be able to factor, the Quadratic Formula can always find the solution to a quadratic equation.
How to Solve the Quadratic Formula
First, we must arrange the quadratic equation in standard-form set equal to zero. In doing so, we organize the equation in such a way so that we can accurately identify the values from the equation that correspond with the formula.
Understanding the Quadratic Formula
Next, we simply plug in these values into the formula and simplify.
That’s it!
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).
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 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.
Quadratic Formula – Video
1 hr 01 min
- Introduction to Video: The Quadratic Formula
- 00:00:21 – Deriving the Quadratic Formula by Completing The Square
- 00:14:07 – Examples #1-4: Solve using the quadratic formula by placing equations in standard form
- 00:29:37 – Examples #5-7: Solve using the quadratic formula with harder equations incorporating leading coefficients and fractions
- 00:43:24 – Examples #8-9: Transform by multiplying polynomial & rational expressions and then solve using the quadratic formula
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