15 questions
10th Grade
Mathematics
Solving with Quadratic Formula is a free printable Grade 10 mathematics worksheet that helps students solve quadratic equations by identifying the coefficients a, b, and c, applying the quadratic formula, and interpreting the discriminant. The 15-item set includes 4 fill-in-the-blank problems and 11 multiple-choice questions, with equations such as 2x² + 2x − 12 = 0 and 2x² − 9x − 35 = 0. Students practise finding two solutions, recognizing when the equation must first be written in standard form, and identifying the discriminant as b² − 4ac. Questions also reinforce that the quadratic formula can solve equations that cannot be factored and that a discriminant of zero produces one real solution. This free printable worksheet includes a complete answer key for Grade 10 instruction, independent practice, review, or assessment.
Worksheet settings
Font size
WorksheetsAnswer Key2, -3
-8 & 4
x= 6, -2
a = 4, b =-8, c =-3
x = -5/2, x = 7
x = -1 and x = -3
True
b2 - 4ac
Real Solution
This Grade 10 worksheet focuses on solving quadratic equations with the quadratic formula through 15 items: 4 fill-in-the-blank problems and 11 multiple-choice questions. Students identify a, b, and c, calculate the discriminant b² − 4ac, determine whether an equation has real solutions, and find both roots of equations such as 2x² − 8x − 24 = 0.
First model how to rewrite an equation in standard form and identify a, b, and c, using the worksheet’s item 4 equation, 2x² + 2x − 12 = 0, as a guided example. Then have students explain how the discriminant affects the solutions before completing the fill-in-the-blank problems and multiple-choice equations independently. Use the coefficient-identification and discriminant questions as quick checks before reviewing the numerical solutions.
Watch for sign errors when students move a constant to standard form, especially in the item involving 4x² − 8x = 3, where c becomes −3. Students may also substitute incorrectly into b² − 4ac, lose the ± when finding two roots, or choose a pair of solutions with reversed signs. The multiple-choice format can reveal whether an error occurred while identifying coefficients, calculating the discriminant, or simplifying the final roots.
The worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can use the same quadratic-formula practice for paper-based or online work. It includes a complete answer key for checking the 4 fill-in-the-blank responses and 11 multiple-choice answers. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.
In the worksheet’s Advanced Settings, adjust font spacing or font size to make the quadratic equations, answer choices, and fill-in-the-blank items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet prompts into another language while retaining the mathematical expressions. These options modify the worksheet file itself without changing the quadratic-formula tasks.
Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
