Question 38

The graph of the function f(x) = -4x^2 + 5 has more than one x-intercept.

This function is a downward-opening parabola, which means it can intersect the x-axis at two points, indicating that it has more than one x-intercept.

A) f(x) = -4x - 5

This function represents a linear equation with a slope of -4 and a y-intercept of -5. A linear function can only intersect the x-axis at one point, thus it cannot have more than one x-intercept.

B) f(x) = -4x ^ 2 + 5

This quadratic function opens downwards, and its graph can intersect the x-axis at two points depending on its vertex position. Specifically, the discriminant of this equation is positive, indicating two x-intercepts.

C) f(x) = 4

This function is a horizontal line at y = 4. Since it does not cross the x-axis at all, it has zero x-intercepts.

D) f(x) = 4x ^ 2 + 5

This function represents a parabola that opens upwards with a vertex above the x-axis. It does not intersect the x-axis at any point, resulting in zero x-intercepts.

E) f(x) = 4x ^ 3 + 5

This cubic function can have up to three x-intercepts, but it does not guarantee more than one. In this case, it has only one real root, thus it does not fulfill the condition of having more than one x-intercept.

Conclusion

The function f(x) = -4x^2 + 5 is the only one among the choices that can intersect the x-axis at two points, confirming it has more than one x-intercept. All other options either produce one or no x-intercepts, making them incorrect answers in this context.