16Hit1600
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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