Can You Find ... Cubic Edition
Can you find a cubic curve that...
(a) ... passes through the $x$-axis at $x=1$ and $x=-1$?
(b) ... passes through the origin and touches the $x$-axis at $x=-3$?
(c) ... touches the $x$-axis at $x=2$ and crosses the $y$-axis at $12$?
(d) ... crosses the $y$-axis at $-6$ and has three integer roots?
(e) ... crosses the $y$-axis at $y=5$ and touches the $x$-axis at $x=1$?
Are any of the curves described above unique?
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.
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