The graph of which of the following functions in the xy-plane has more than one x-intercept?
f(x) = -4x² + 5 has more than one x-intercept.
This quadratic function opens downward and has a maximum point, allowing it to intersect the x-axis at two points, thus yielding two x-intercepts.
This linear function has a slope of -4 and a y-intercept of -5. As a linear equation, it can have only one x-intercept, which occurs where the line crosses the x-axis. Therefore, it does not meet the criteria of having more than one x-intercept.
This quadratic function opens downward due to the negative leading coefficient. The maximum value occurs at the vertex, and because it crosses the x-axis at two points, it has two x-intercepts, satisfying the question's condition.
This constant function has a value of 4 for all x, meaning it does not intersect the x-axis at all. Consequently, there are no x-intercepts, as the graph is a horizontal line above the x-axis.
This quadratic function opens upward, and since the vertex is above the x-axis (minimum value of 5), it does not intersect the x-axis at any point. Therefore, it has no x-intercepts.
This cubic function has a positive leading coefficient and will intersect the x-axis at most once. The graph can have one real root, but it does not reach more than one x-intercept as it does not curve back down to cross the x-axis again.
Among the provided functions, only f(x) = -4x² + 5 has the characteristic of more than one x-intercept due to its downward-opening parabola. The other options, whether linear, constant, or upward-opening quadratics, each demonstrate either one x-intercept or none at all, affirming that the only function satisfying the condition is option B.
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