Advanced MathMediumFunction from its zeros and y-intercept
Advanced Math practice question
A quadratic function has zeros at x = 2 and x = −3, and its graph crosses the y-axis at (0, −6). Which equation defines the function?
- A. y = (x − 2)(x + 3)Correct
- B. y = (x + 2)(x − 3)
- C. y = −(x − 2)(x + 3)
- D. y = (x − 2)(x − 3)
Answer: A. y = (x − 2)(x + 3)
Zeros 2 and −3 give factors (x − 2)(x + 3). At x = 0 this is (−2)(3) = −6 ✓.
Why the other answers are wrong
- B. y = (x + 2)(x − 3)
- (x + 2)(x − 3) has zeros −2 and 3.
- C. y = −(x − 2)(x + 3)
- The negative sign gives y-intercept +6, not −6.
- D. y = (x − 2)(x − 3)
- (x − 2)(x − 3) has zeros 2 and 3 and y-intercept 6.
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