Advanced MathMediumMatching a description to an equation
Advanced Math practice question
Which of the following equations has a graph in the xy-plane that opens downward and has its vertex on the x-axis?
- A. y = −(x − 2)²Correct
- B. y = (x − 2)²
- C. y = −(x − 2)² + 1
- D. y = −x² + 2
Answer: A. y = −(x − 2)²
The negative sign in front makes the parabola open downward, and the vertex of y = −(x − 2)² is (2, 0), which lies on the x-axis.
Why the other answers are wrong
- B. y = (x − 2)²
- y = (x − 2)² has its vertex on the x-axis but opens UPWARD.
- C. y = −(x − 2)² + 1
- The +1 lifts the vertex to (2, 1), off the x-axis.
- D. y = −x² + 2
- y = −x² + 2 opens downward but its vertex is (0, 2), above the x-axis.
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