Advanced MathVery hardArea of the triangle formed by a parabola's intercepts and vertex
Advanced Math practice question
In the xy-plane, the graph of y = −x² + 6x − 5 has two x-intercepts and a vertex. What is the area of the triangle whose vertices are those three points?
Answer: 8
The x-intercepts are at x = 1 and x = 5 (base 4). The vertex is at x = 3, where y = −9 + 18 − 5 = 4 (height 4). Area = (1/2)(4)(4) = 8.
Common wrong answers
- If you answered 4
- 4 is the height, or the base, alone.
- If you answered 12
- 12 uses a base of 6 (the sum of the intercepts).
- If you answered 16
- 16 forgets the 1/2.
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