Advanced MathMediumy-intercept of a quadratic
Advanced Math practice question
The function f is defined by f(x) = 2x² − 8x + 3. What is the y-coordinate of the y-intercept of the graph of f in the xy-plane?
- A. 3Correct
- B. −8
- C. 2
- D. −3
Answer: A. 3
The y-intercept is where x = 0. Substituting: f(0) = 2(0)² − 8(0) + 3 = 3. In standard form ax² + bx + c, the y-intercept is always the constant c.
Why the other answers are wrong
- B. −8
- −8 is the coefficient of x. It controls the slope near the intercept, but at x = 0 the term −8x vanishes.
- C. 2
- 2 is the leading coefficient. It sets how steeply the parabola opens, not where it crosses the y-axis.
- D. −3
- The constant is +3. Perhaps the sign was borrowed from the −8x term; substituting x = 0 leaves exactly +3.
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