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NRICH: Inside a Parabola

A triangle of area 64 square units is drawn inside the parabola y=k2−x2. Find the value of k.

The points where the parabola y=k2−x2 crosses the coordinate axes are joined to form a triangle.


The area of the triangle is 64 square units. What is the value of k?

This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Age 14 to 16

STEAM Topics Resource Audience Grade Level Tags
Math Topics
Algebra & Pre-Algebra, Functions & Graphs, Quadratic Equations
High School, Educator
9th Grade, 10th Grade, 11th Grade
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