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Function f is a quadratic function passing through the points (-4,0) , (0,-12) , (3,0). Function g is modeled by the graph.
Graph shows downward parabola plotted on a coordinate plane. The parabola has vertex at (minus 2, 9). The parabola has left slope at (minus 5, 0) and right slope at (1, 0).
Over which interval are both functions negative?
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To determine the interval over which both functions f and g are negative, we need to find where both graphs are below the x-axis.
For function f, since it is a quadratic function, the vertex lies at the axis of symmetry. In this case, the axis of symmetry is x = -4. Since the point (0, -12) is on the graph, we can see that the graph opens upwards. Therefore, for function f, the part of the graph that lies below the x-axis is between x = -4 and x = 3.
For function g, we are given that it is a downward parabola and its vertex is (-2, 9). Since the graph opens downwards, the part of the graph that lies below the x-axis is the interval between x = -5 and x = 1.
To find the interval where both functions are negative, we need to find their overlap. By inspecting the graphs, we can see that the common interval where both functions are below the x-axis is between x = -4 and x = -2.
Therefore, the interval over which both functions f and g are negative is (-4, -2).