3
QuizMultiple Choice

Quadratic Functions: Standard Form

Question 3 • High School Math 2 A

For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?

Answer
A
The graph will always have zero x-intercepts.
B
The function will always have a minimum.
C
The y-intercept will always be the vertex.
D
The axis of symmetry will always be positive.

Explanation

When b = 0, the function is f(x) = ax² + c. Its vertex occurs at x = −b/(2a) = 0, so the vertex is (0, c). The y-intercept is also found by setting x = 0, which gives (0, c), so the y-intercept is always the vertex. The graph may have a maximum rather than a minimum if a is negative, so B is not always true.

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