Advanced MathMediumy-intercept from the x-intercepts of a monic quadratic
Advanced Math practice question
The graph of f(x) = x² + bx + c in the xy-plane has x-intercepts at x = −2 and x = 6, where b and c are constants. What is the y-intercept of the graph?
Answer: -12
With leading coefficient 1 and roots −2 and 6, f(x) = (x + 2)(x − 6) = x² − 4x − 12. The y-intercept is f(0) = −12.
Common wrong answers
- If you answered 4
- 4 is the sum of the roots.
- If you answered 12
- 12 has the wrong sign: (2)(−6) = −12.
- If you answered -4
- −4 is b, the coefficient of x.
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