The Quadratic Formula

The Quadratic Formula

The quadratic formula is a formula which we can use to solve almost any quadratic equation. This is the quadratic formula. It is usually written without brackets but just to make it easier to use and understand, we have included the brackets. Every letter represents a quadratic coefficient (ax²+bx+c). To find the two answers of a quadratic equation, you simply need to replace the letters with the quadratic coefficients and solve the equation.

Solving Quadratic Equations using the Quadratic Formula

To solve a quadratic equation using the quadratic formula, we first need to find the values of a,b and c. In this case they are 2, -3 and -4. Now we replace the letters in the quadratic formula with the correct number and simplify it as much as possible without solving it. For the next step, you may need a calculator depending on the number that is to be square rooted (in this case, we have sqrt of 41 which gives us a decimal answer that we cannot calculate in our heads). You have to now type the equation into your calculator once with a minus sign and once with a plus sign instead of the plus or minus sign. The answers that you get from these two equations are the solutions to the quadratic equation.
It is always good to use the quadratic formula as you can even solve quadratic equations which cannot be solved using factorisation. However, in some cases, it may be easier to use factorisation. It depends on which technique you think you are more comfortable with.

Graphically Solving Quadratics

There is another method which you can use to solve quadratic equations. It is called solving quadratics graphically. We recommend that you give this method a try. Please share this page if you like it or found it helpful!
Example 1 In this example, we have found the quadratic coefficients and replaced them with the letters in the formula. We have then simplified the formula. Next we solved it, once with a plus sign and once with an equal sign. We did not necessarily have to use a calculator as the sqrt of 49 is 7.
Example 2 We have solved this quadratic equation by identifying the quadratic coefficients and substituting them into the quadratic formula. We have then simplified and solve the quadratic formula to get the two solutions to the quadratic equation. Again, we did not have to use a calculator as the sqrt of 81 is 9 (easy to calculate).
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Chapter 17.2:  Learning Outcomes Students will be introduced to the quadratic formula! Students will learn how to solve quadratics that do not factorise using the quadratic formula!



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