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Quadratic Equations Adventure
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Quadratic Equations Adventure
Arjun, Grace and Matilda are testing designs in a library makerspace. Solve each quadratic challenge. Show working for questions that ask you to solve or explain. Give exact answers unless a question asks for a decimal approximation.
1.A design program has solutions x = 3 and x = −2. Write a monic quadratic equation with exactly these solutions, in the form ax² + bx + c = 0.
2.Grace is deciding how to solve x² + 7x + 12 = 0. Which method is most efficient?
- Factorising
- Completing the square
- Using the quadratic formula
3.Factorise x² + 7x + 12, then use your factors to solve x² + 7x + 12 = 0. Show both solutions.
4.The solutions to a quadratic are x = −4 and x = 2. Mark both roots on the number line. Then write the monic quadratic equation with those roots.
5.Matilda needs to solve x² + 5x + 7 = 0. Calculate the discriminant b² − 4ac. What does its value tell you about the number of real solutions?
6.Arjun says x² − 9 = 0 has only one solution because the constant term is negative. Is he correct? Solve the equation and explain briefly.
7.Use the quadratic formula to solve 2x² + 3x − 2 = 0. Show your substitution and give both solutions.
8.A small foam prototype is launched from a platform. Its height is h = −5t² + 20t + 1, where h is in metres and t is in seconds. Find the time when it reaches its maximum height, then calculate that height. Use the vertex formula t = −b/(2a).
9.Write a monic quadratic equation whose solutions are x = −1 and x = 6. Expand your factors and check that your equation has the stated solutions.
2 printable pages
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