Advanced MathVery hardSum of y-coordinates where a parabola meets a line
Advanced Math practice question
The parabola y = x² − 2x and the line y = x + 4 meet at points P and Q. What is the sum of the y-coordinates of P and Q?
Answer: 11
Set equal: x² − 2x = x + 4, so x² − 3x − 4 = 0, (x − 4)(x + 1) = 0. At x = 4, y = 8; at x = −1, y = 3. Sum: 8 + 3 = 11.
Common wrong answers
- If you answered 3
- 3 is the sum of the x-coordinates (4 + (−1)), not the y-coordinates.
- If you answered 8
- 8 is only P's y-coordinate; Q's is 3.
- If you answered -4
- −4 is the product of the x-coordinates.
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