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Advanced MathVery hardOther intercept from the vertex

Advanced Math practice question

A parabola has its vertex at (4, −9) and passes through (1, 0). What is the x-coordinate of its other x-intercept?

Answer: 7

By symmetry about x = 4, the intercept at x = 1 (three left of the axis) pairs with one three to the right: x = 7.

Common wrong answers

If you answered 8
The known intercept is 3 units from the axis, so the other is at 4 + 3 = 7.
If you answered 9
9 is the vertex's depth |−9|, not an intercept.
If you answered -1
Reflect across the axis x = 4, not across the y-axis.

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