(x+4)(x-2)²(x+3) (option D)
Explanation:To determine which polynomial was graphed, we look at the roots of the function on the graph with the options given.
The roots of the equation are the x values that make the function equal to zero.
On the graph, we check the values of the line that crosses the x axis.
Each box on the x axis represents 2 units
we have x = 2 (towards the right of the x-axis).
Note that two lines touched x = 2. This means x =2 appeared twice
we also have x = -4 (towards the left x axis)
Then we have value of x that is before the x = -4. Checking the options, the value of x will be equal to -3
Now we rewrite:
x = 2, x = 2, x = -4, x = -3
x-2 = 0, x-2 = 0, x + 4 = 0, x+3 = 0
The roots of the function:
(x-2)²(x+4)(x+3)
Hence, the polynomial functions graphed below is (x+4)(x-2)²(x+3) (option D)
