Quadratic Formula Worksheets

Free Practice Using the Quadratic Formula Worksheets with Answers

Do you or your students need some extra practice with solving quadratic equations using the Quadratic Formula?

If so, this page shares a free collection of printable Quadratic Formula Worksheets that can be downloaded as PDF files. Each quadratic formula worksheet includes a reference box at the top of the page that shares the quadratic formula, ten unique practice problems, and a complete answer key so that you or your students can check answers and assess your under understanding of how to solve quadratic equations using the quadratic formula.

If you need a quick reference, the quadratic formula states that for any equation of the form ax² + bx + c = 0 (where a ≠ 0), the following is true:

• x= (-b ± [√(b² - 4ac)]) / 2a

If you need a more in-depth review of how to use the quadratic formula, the second section of this guide includes a short recap of key vocabulary terms as well as step-by-step examples of how to use the quadratic formula.

Any free quadratic formula worksheet can be previewed, downloaded, and/or printed simply by clicking any of the blue text links in the worksheet library below. When you click on one of the blue text links, a preview window will appear and you will have the option to save the PDF file to your device and/or send the file to your printer. If printing, you have the option of printing the first page (the practice problem page) and/or the second page (the corresponding answer key).

All of the free quadratic formula worksheets are sample activities from the Mashup Math Algebra Infinite Worksheet Libraries available on our website. | Quick Reference: How to Download/Print

Quadratic Formula Worksheets

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Quadratic Formula Worksheet Review

If you are having a hard time solving problems on a quadratic formula worksheet, then you will likely find this quick review very helpful.

In algebra, the quadratic formula, x= (-b ± [√(b² - 4ac)]) / 2a, is a handy tool that you can use to find the roots, or solutions, of a quadratic equation of the form ax² + bx + c = 0 (where a ≠ 0). Additionally, if a given equation is not in ax² + bx + c = 0 form, you can often rearrange the terms using some simple algebra so that it is in ax² + bx + c = 0, which would then allow you to use the quadratic formula.

Why is the quadratic formula so useful? As you may know, some quadratic functions can be very easy to factor and solve, while others can be very difficult. The quadratic formula, however, can be used to find the solutions to any quadratic equation, whether it is easy to factor or not. So, if you struggle with factoring quadratic equations, then the quadratic formula is an awesome tool that you can use to solve a variety of problems involving quadratics.

The quadratic formula is also incredibly useful because it can be used to find not only real solutions to quadratic functions, but imaginary and complex solutions as well, making it one of the most important and helpful algebra formulas that you will ever learn.

The quadratic formula is illustrated using color coding in Figure 01 below. Make sure that you memorize this formula correctly and that you know it by heart so that you can recall it and use it correctly whenever you need to.

Now that you know the quadratic formula and why it is so useful, let’s go ahead and gain some practice using it to find the solutions of a given quadratic function.

Example: Use the quadratic formula to solve this equation: x² -9x + 20 = 0

For starters, notice that the equation is already in ax² + bx + c = 0 form, where:

• a=1

• b=-9

• c=20

Now that we know the values of a, b, and c, we can substitute them into the quadratic formula as follows:

• x= (-b ± [√(b² - 4ac)]) / 2a

• x= (-(-9) ± [√((-9)² - 4(1)(20))]) / 2(1)

• x= (9 ± [√(81-80)]) / 2

• x= (9 ± √(1)) / 2

• x= (9 ± 1) / 2

From here, we can split the ± sign (meaning “plus or minus”) to create two equations that we can solve. If both equations give the same result for x, then the quadratic function has only one solution. If both results are different, then the quadratic will have two solutions.

• Plus: x= (9 + 1) / 2 → 10/2 → x=5

• Minus: x= (9 - 1) / 2 → 8/2 → x=4

In this example, we have two solutions: x=5 or x=4 and we can conclude that…

Final Answer: x² -9x + 20 = 0 has solutions at x=5 and x=4.

And that’s all that there is to it! Now that you have reviewed how to use the quadratic formula, go ahead and work through a quadratic formula worksheet from the free library above to get some more practice. The more that you use the quadratic formula to solve problems, the better at using it you will become!