Which of the following accurately describes what the graph of y = 5x^2 + 50x + 125 looks like, with the repeated root of x = -5? Pick the correct answer.
Statement #1: The graph opens downward.
Statement #2: The graph has a vertex to the right of the x-axis.
Statement #3: The graphs touches the x-axis once.
Statement #1: The graph opens downward. This statement is true because the leading coefficient of the quadratic equation is positive (5), indicating that the graph will open upward.
Statement #2: The graph has a vertex to the right of the x-axis. This statement is false. Since the repeated root of x = -5 is given, it means that the quadratic function has a double root. Therefore, the vertex of the parabola will be at x = -5, which is on the x-axis.
Statement #3: The graphs touches the x-axis once. This statement is false. Since the graph has a repeated root of x = -5, it means that the graph touches the x-axis at x = -5, but does not intersect it at any other point. Therefore, the graph touches the x-axis once.
So, the correct answers are:
Statement #1: The graph opens downward.
Statement #3: The graph touches the x-axis once.