Advanced MathHardVertex and intercepts from vertex form
Advanced Math practice question
The function w is defined by w(x) = (x + 1)² − 4. Which statement about the graph of y = w(x) is true?
- A. Its vertex is (−1, −4), and it crosses the x-axis at x = 1 and x = −3.Correct
- B. Its vertex is (1, −4), and it crosses the x-axis at x = −1 and x = 3.
- C. Its vertex is (−1, 4), and it does not cross the x-axis.
- D. Its vertex is (−1, −4), and it crosses the x-axis at x = 2 and x = −2.
Answer: A. Its vertex is (−1, −4), and it crosses the x-axis at x = 1 and x = −3.
Vertex form (x − h)² + k with h = −1, k = −4. Zeros: (x + 1)² = 4, x + 1 = ±2, x = 1 or −3.
Why the other answers are wrong
- B. Its vertex is (1, −4), and it crosses the x-axis at x = −1 and x = 3.
- (x + 1)² has its vertex at x = −1, not 1.
- C. Its vertex is (−1, 4), and it does not cross the x-axis.
- The −4 puts the vertex below the axis, so it does cross.
- D. Its vertex is (−1, −4), and it crosses the x-axis at x = 2 and x = −2.
- ±2 are the values of x + 1, not of x.
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