Why does my child think y = (x − 2)² + 5 turns at (−2, 5)?
Your child changes the sign in the bracket when reading a turning point, such as taking y = (x − 2)² + 5 to turn at (−2, 5) instead of (2, 5).
Why children do it
The −2 is right there in the equation, so it's natural to read it off. But the curve is lowest where the bracket is 0, and x − 2 is 0 when x = 2. So the turning point is (2, 5): the sign in the bracket is the opposite of the x-coordinate. Asking which x makes the bracket 0 finds it.
How to help at home
Ask them which x makes the bracket 0. For (x − 2)², it's 2, so the curve turns at x = 2.
The right way
What is the turning point of y = (x − 3)² − 2?
- (3, −2)The bracket is 0 when x = 3, and then y = -2.
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