Advanced MathHardProduct of intersection x-coordinates
Advanced Math practice question
In the xy-plane, the graphs of y = x² − 3x and y = 4 intersect at two points. What is the product of the x-coordinates of those two points?
Answer: -4 or −4
Set the expressions equal: x² − 3x = 4, so x² − 3x − 4 = 0, which factors as (x − 4)(x + 1) = 0. The x-coordinates are 4 and −1, and their product is −4.
Common wrong answers
- If you answered 3
- 3 is the SUM of the x-coordinates (4 + (−1)). The question asks for the product.
- If you answered 4
- 4 is one of the x-coordinates (and also the y-value of the line). The other x-coordinate is −1, and 4 × (−1) = −4.
- If you answered -3
- −3 has the wrong sign for the sum and isn't the product either. Factor x² − 3x − 4 as (x − 4)(x + 1).
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