Advanced MathVery hardConstant that places a parabola's vertex on a given line
Advanced Math practice question
In the xy-plane, the vertex of the graph of y = x² − 8x + c lies on the line y = x, where c is a constant. What is the value of c?
Answer: 20
The vertex is at x = 4, where y = 16 − 32 + c = c − 16. On y = x, this equals 4: c − 16 = 4, so c = 20.
Common wrong answers
- If you answered 4
- 4 is the vertex's x-coordinate, not c.
- If you answered 12
- 12 comes from c − 16 = −4, a sign slip.
- If you answered 16
- 16 puts the vertex on the x-axis (y = 0), not on y = x.
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