Final answer:
To sketch a graph of a degree 5 polynomial with 5 real zeros and a negative leading coefficient, plot the zeros on the x-axis and connect them with a downward trend to the right.
Step-by-step explanation:
To sketch a graph of a degree 5 polynomial with 5 real zeros and a negative leading coefficient, we need to consider the properties of polynomial graphs. Firstly, a degree 5 polynomial will have at most 5 real zeros.
With 5 real zeros, we know that the graph will intersect the x-axis at these points. Secondly, a negative leading coefficient will result in the graph trending downwards as x approaches negative infinity.
Let's represent the 5 real zeros as x1, x2, x3, x4, and x5. To sketch the graph, we will plot the points (-x1, 0), (-x2, 0), (-x3, 0), (-x4, 0), and (-x5, 0) on the x-axis.
Then, we will use the trend of the graph to connect these points, ensuring it goes downward to the right.
For example, if the real zeros are x1 = -2, x2 = -1, x3 = 0, x4 = 1, and x5 = 2, the graph would intersect the x-axis at (-2, 0), (-1, 0), (0, 0), (1, 0), and (2, 0) respectively. Connecting these points, the graph would trend downward to the right.