Which of the following graphs in the xy-plane have -3 and 5 as all of their distinct zeros for -6

Question

Which of the following graphs in the  xy-plane have -3 and 5 as all of their distinct zeros for  -6 <= x <= 6 ?

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Problem Understanding: Understand the problem. We need to find the graphs that have -3 and 5 as their only zeros within the interval -6 <= x <= 6. This means that the graph should touch or cross the x-axis at x = -3 and x = 5, and not at any other point within the given interval.General Form of the Polynomial: Determine the general form of the polynomial. A polynomial that has -3 and 5 as zeros can be written as f(x) = a(x + 3)(x - 5), where a is a non-zero constant. The value of a will affect the width and direction of the graph but not the zeros.Additional Requirements: Check for additional requirements. Since the problem only specifies that -3 and 5 are the distinct zeros and does not mention any other conditions, any graph of the form f(x) = a(x + 3)(x - 5) with a ≠ 0 will satisfy the condition as long as it does not cross the x-axis at any other point within the interval -6 <= x <= 6.Behavior at the Zeros: Determine the behavior of the graph at the zeros. At x = -3, the graph should either touch or cross the x-axis, and the same goes for x = 5. If a > 0, the graph will open upwards, and if a < 0, the graph will open downwards.Behavior Outside the Zeros: Verify the behavior of the graph outside the zeros. For x < -3, the graph should be above the x-axis if a > 0 and below the x-axis if a < 0. For -3 < x < 5, the graph should be below the x-axis if a > 0 and above the x-axis if a < 0. For x > 5, the graph should be above the x-axis if a > 0 and below the x-axis if a < 0.Graph Characteristics: Conclude the characteristics of the graph. The graph of f(x) = a(x + 3)(x - 5) will have -3 and 5 as its zeros, and it will not have any other zeros within the interval -6 <= x <= 6. The graph will either open upwards or downwards depending on the sign of a, but this does not affect the location of the zeros.

Which of the following graphs in the $x y$ -plane have $-3$ and $5$ as all of their distinct zeros for $-6 \leq x \leq 6$ ?

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Which of the following graphs in the $x y$ -plane have $-3$ and $5$ as all of their distinct zeros for $-6 \leq x \leq 6$ ?